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Axiomatizability of the Class of Subdirectly Irreducible S-Acts over a Commutative Monoid Algebra Logic (IF 0.5) Pub Date : 2024-02-16
An axiomatizability criterion is found for the class of subdirectly irreducible S-acts over a commutative monoid. As a corollary, a number of properties are presented which a commutative monoid should satisfy provided that the class of subdirectly irreducible acts over it is axiomatizable. The question about a complete description of monoids over which the class of subdirectly irreducible acts is axiomatizable
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An Explicit Basis for WCP-Globally Admissible Inference Rules Algebra Logic (IF 0.5) Pub Date : 2024-02-15 V. V. Rimatskii
Inference rules are examined which are admissible immediately in all residually finite extensions of S4 possessing the weak cocover property. An explicit basis is found for such WCP-globally admissible rules. In case of tabular logics, the basis is finite, and for residually finite extensions, the independency of an explicit basis is proved.
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Varieties of Exponential R-Groups Algebra Logic (IF 0.5) Pub Date : 2024-02-15 M. G. Amaglobeli, A. G. Myasnikov, T. T. Nadiradze
The notion of an exponential R-group, where R is an arbitrary associative ring with unity, was introduced by R. Lyndon. Myasnikov and Remeslennikov refined the notion of an R-group by introducing an additional axiom. In particular, the new concept of an exponential MR-group (R-ring) is a direct generalization of the concept of an R-module to the case of noncommutative groups. We come up with the notions
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Horizontal Joinability on 5-Dimensional 2-Step Carnot Groups with a Codimension 2 Horizontal Distribution Algebra Logic (IF 0.5) Pub Date : 2024-02-15
For a 5-dimensional 2-step Carnot group G3,2 with a codimension 2 horizontal distribution, we prove that any two points u, v ∈ G3,2 can be joined on it by a horizontal broken line consisting of at most three segments. A multi-dimensional generalization of this result is given.
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Generalized Schur Groups Algebra Logic (IF 0.5) Pub Date : 2024-02-14 G. K. Ryabov
An S-ring (Schur ring) is said to be central if it is contained in the center of a group ring. We introduce the notion of a generalized Schur group, i.e., a finite group such that all central S-rings over this group are Schurian. It generalizes the notion of a Schur group in a natural way, and for Abelian groups, the two notions are equivalent. We prove basic properties and present infinite families
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The Complexity of Inversion in Groups Algebra Logic (IF 0.5) Pub Date : 2024-02-13 P. E. Alaev
We prove that if \(\mathcal{A}\) = (A,⋅) is a group computable in polynomial time (P-computable), then there exists a P-computable group \(\mathcal{B}\) = (B,∙) ≅ \(\mathcal{A},\) in which the operation x−1 is also P-computable. On the other hand, we show that if the center \(Z\left(\mathcal{A}\right)\) of a group A contains an element of infinite order, then under some additional assumptions, there
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Splitting of Normalizers of Maximal Tori in Finite Groups of Lie Type Algebra Logic (IF 0.5) Pub Date : 2024-01-05 A. A. Galt, A. M. Staroletov
Let G be a finite group of Lie type, and T some maximal torus of the group G. We bring to a close the study of the question of whether there exists a complement for a torus T in its algebraic normalizer N (G, T). It is proved that any maximal torus of a group G ∈ {G2(q), 2G2(q), 3D4(q)} has a complement in its algebraic normalizer. Also we consider the remaining twisted classical groups 2An(q) and
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Finite Groups with a Soluble Group of Coprime Automorphisms Whose Fixed Points Have Bounded Engel Sinks Algebra Logic (IF 0.5) Pub Date : 2024-01-04 E. I. Khukhro, P. Shumyatsky
Suppose that a finite group G admits a soluble group of coprime automorphisms A. We prove that if, for some positive integer m, every element of the centralizer CG(A) has a left Engel sink of cardinality at most m (or a right Engel sink of cardinality at most m), then G has a subgroup of (|A|,m)-bounded index which has Fitting height at most 2α(A) + 2, where α(A) is the composition length of A. We
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Toward a Sharp Baer–Suzuki Theorem for the π-Radical: Exceptional Groups of Small Rank Algebra Logic (IF 0.5) Pub Date : 2024-01-04 Zh. Wang, W. Guo, D. O. Revin
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Generic Types and Generic Elements in Divisible Rigid Groups Algebra Logic (IF 0.5) Pub Date : 2024-01-03 A. G. Myasnikov, N. S. Romanovskii
A group G is said to be m-rigid if it contains a normal series of the form G = G1 > G2 > . . . > Gm > Gm+1 = 1, whose quotients Gi/Gi+1 are Abelian and, treated as (right) ℤ[G/Gi]-modules, are torsion-free. A rigid group G is said to be divisible if elements of the quotient ρi(G)/ρi+1(G) are divisible by nonzero elements of the ring ℤ[G/ρi(G)]. Previously, it was proved that the theory of divisible
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Finite 4-Primary Groups with Disconnected Gruenberg–Kegel Graph Containing a Triangle Algebra Logic (IF 0.5) Pub Date : 2024-01-03 A. S. Kondrat’ev
We give a description of finite 4-primary groups with disconnected Gruenberg–Kegel graph containing a triangle. As a corollary, finite groups whose Gruenberg–Kegel graph coincides with the Gruenberg–Kegel graph of 3D4(2) are exemplified, which generalizes V. D. Mazurov’ description of finite groups isospectral to the group 3D4(2).
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Primitive Prime Divisors of Orders of Suzuki–Ree Groups Algebra Logic (IF 0.5) Pub Date : 2024-01-03
There is a well-known factorization of the number 22m + 1, with m odd, related to the orders of tori of simple Suzuki groups: 22m +1 is a product of a = 2m + 2(m+1)/2 +1 and b = 2m − 2(m+1)/2 + 1. By the Bang–Zsigmondy theorem, there is a primitive prime divisor of 24m − 1, that is, a prime r that divides 24m − 1 and does not divide 2i − 1 for any 1 ≤ i < 4m. It is easy to see that r divides 22m +
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Shunkov Groups Saturated with Almost Simple Groups Algebra Logic (IF 0.5) Pub Date : 2023-12-28 N. V. Maslova, A. A. Shlepkin
A group G is called a Shunkov group (a conjugate biprimitive finite group) if, for any of its finite subgroups H in the factor group NG(H)/H, every two conjugate elements of prime order generate a finite subgroup. We say that a group is saturated with groups from the set 𝔐 if any finite subgroup of the given group is contained in its subgroup isomorphic to some group in 𝔐. We show that a Shunkov
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Unsolvability of Finite Groups Isospectral to the Automorphism Group of the Second Sporadic Janko Group Algebra Logic (IF 0.5) Pub Date : 2023-12-28
For a finite group G, the spectrum is the set ω(G) of element orders of the group G. The spectrum of G is closed under divisibility and is therefore uniquely determined by the set μ(G) consisting of elements of ω(G) that are maximal with respect to divisibility. We prove that a finite group isospectral to Aut(J2) is unsolvable.
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Families of Permutations and Ideals of Turing Degrees Algebra Logic (IF 0.5) Pub Date : 2023-12-04 A. S. Morozov, V. G. Puzarenko, M. Kh. Faizrachmanov
Families 𝒫I consisting of permutations of the natural numbers ω whose degrees belong to an ideal I of Turing degrees, as well as their jumps \({\mathcal{P}}_{\mathrm{I}}{\prime}\), are studied. For any countable Turing ideal I, the degree spectra of families 𝒫I and their jumps \({\mathcal{P}}_{\mathrm{I}}{\prime}\) are described. For some ideals I generated by c.e. degrees, the spectra of families
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Normal Companions of Intuitionistic Modal Logics Algebra Logic (IF 0.5) Pub Date : 2023-11-23 S. A. Drobyshevich
Previously, Došen and Božić introduced four independent intuitionistic modal logics, one for each of four types of modal operators—necessity N, possibility P, impossibility Im, and unnecessity Un. These logics are denoted HKM, where M ∈ {N, P, Un, Im}. Interest in treating the four types of modal operators separately is associated with just the fact that these cannot be reduced to each other over intuitionistic
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Generic Complexity of the Word Problem in Some Semigroups Algebra Logic (IF 0.5) Pub Date : 2023-11-15 A. N. Rybalov
Generic algorithms decide problems on sets of almost all inputs, outputting an indefinite answer for other rare inputs. We will prove that the word problem is generically decidable in finitely generated semigroups 𝔖, for which there exists a congruence θ such that the semigroup 𝔖/θ is an infinite residually finite monoid with cancellation property and decidable word problem. This generalizes the
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Structure of Singular Superalgebras with 2-Dimensional Even Part and New Examples of Singular Superalgebras Algebra Logic (IF 0.5) Pub Date : 2023-11-08 S. V. Pchelintsev, O. V. Shashkov
It is proved that a singular superalgebra with a 2-dimensional even part is isomorphic to a superalgebra B2|3(φ, ξ, ψ). In particular, there do not exist infinite-dimensional simple singular superalgebras with a 2-dimensional even part. It is proved that if a singular superalgebra contains an odd left annihilator, then it contains a nondegenerate switch. Lastly, it is established that for any number
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Cardinality Reduction Theorem for Logics QHC and QH4 Algebra Logic (IF 0.5) Pub Date : 2023-11-08 A. A. Onoprienko
The joint logic of problems and propositions QHC introduced by S. A. Melikhov, as well as intuitionistic modal logic QH4, is studied. An immersion of these logics into classical first-order predicate logic is considered. An analog of the Löwenheim–Skolem theorem on the existence of countable elementary submodels for QHC and QH4 is established.
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A Class of Generalized Derivations Algebra Logic (IF 0.5) Pub Date : 2023-11-03 A. S. Zakharov
We consider a class of generalized derivations that arise in connection with the problem of adjoining unity to an algebra with generalized derivation, and of searching envelopes for Novikov–Poisson algebras. Conditions for the existence of the localization of an algebra with ternary derivation are specified, as well as conditions under which given an algebra with ternary derivation, we can construct
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Generalized Stability of the Class of Injective S-Acts Algebra Logic (IF 0.5) Pub Date : 2023-11-01 A. A. Stepanova
The concept of P-stability is a particular case of generalized stability of complete theories. We study injective S-acts with a P-stable theory. It is proved that the class of injective S-acts is (P, 1)-stable only if S is a one-element monoid. Also we describe commutative and linearly ordered monoids S the class of injective S-acts over which is (P, s)-, (P, a)-, and (P, e)-stable.
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Modification and Correction of Medvedev’s Example of a Solvable Alternative Algebra Algebra Logic (IF 0.5) Pub Date : 2023-09-06 I. P. Shestakov
Yu. A. Medvedev [Algebra and Logic, 19, No. 3, 191—201 (1980)] constructed an example of alternative algebra that he used to prove that a certain variety of alternative algebras possess the non-Specht property over a field of characteristic 2. Though his result concerned the characteristic 2 case, the example was claimed to be alternative over an arbitrary field, and it was later used by V. T. Filippov
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Partial Hopf–Galois Theory Algebra Logic (IF 0.5) Pub Date : 2023-09-04 F. Castro, D. Freitas, A. Paques, G. Quadros, T. Tamusiunas
A partial Hopf–Galois theory is developed for partial H-module algebras, and we recover analogs of classical results for Hopf algebras.
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Dynamic Temporal Logical Operations in Multi-Agent Logics Algebra Logic (IF 0.5) Pub Date : 2023-08-30 V. V. Rybakov
We study temporal multi-agent logics using a new approach to defining time for individual agents. It is assumed that in any time state each agent (in a sense) generates its own future time, which will only be available for analysis in the future. That is, the defined time interval depends both on the agent and on the initial state where the agent starts to act. It is also assumed that the agent may
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Pre-Minimal Pairs and Homogeneous Valuations Algebra Logic (IF 0.5) Pub Date : 2023-08-30 Yu. L. Ershov
We offer for consideration and study the concept of a pre-minimal pair. Also we examine extensions of valuations of a field F to valuations of the rational function field F(x) in one variable.
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On the Absoluteness of ℵ1-Freeness Algebra Logic (IF 0.5) Pub Date : 2023-08-25 D. Herden, A. V. Pasi
ℵ1-free groups, Abelian groups for which every countable subgroup is free, exhibit a number of interesting algebraic and set-theoretic properties. We will give a complete proof that the property of being ℵ1-free is absolute; that is, if an Abelian group G is ℵ1-free in some transitive model M of ZFC, then it is ℵ1-free in any transitive model of ZFC containing G. The absoluteness of ℵ1-freeness has
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A Class of Low Linear Orders Having Computable Presentations Algebra Logic (IF 0.5) Pub Date : 2023-08-23 M. V. Zubkov
It is shown that any low linear order of the form \(\mathcal{L}\)+ω∗, where \(\mathcal{L}\) is some η-presentation, has a computable copy. This result contrasts with there being low η-presentations not having a computable copy.
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Complexity of the Problem of Being Equivalent to Horn Formulas. II Algebra Logic (IF 0.5) Pub Date : 2023-04-28 N. T. Kogabaev
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Versions of a Local Contraction Subexponential in the Lambek Calculus Algebra Logic (IF 0.5) Pub Date : 2023-04-26 M. V. Valinkin
The Lambek calculus was introduced as a tool for examining linguistic constructions. Then this calculus was complemented with both new connectives and structural rules like contraction, weakening, and permutation. The structural rules are allowed only for formulas under the symbol of a specific modality called exponential. The Lambek calculus itself is a noncommutative structural logic, and for arbitrary
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Algebraic Properties of Subquasigroups and Construction of Finite Quasigroups Algebra Logic (IF 0.5) Pub Date : 2023-04-24 V. A. Artamonov, S. Chakrabarti, Sh. K. Tiwari, V. T. Markov
Many important properties are identified and criteria are developed for the existence of subquasigroups in finite quasigroups. Based on these results, we propose an effective method that concludes the nonexistence of proper subquasigroups in a given finite quasigroup, or finds all its proper subquasigroups. This has an important application in checking the cryptographic suitability of a quasigroup
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Boolean Algebras Autostable Relative to n-Decidable Presentations Algebra Logic (IF 0.5) Pub Date : 2023-04-20 M. N. Gaskova
We give an algebraic description of Boolean algebras autostable relative to n-decidable presentations. Also, autostable Iλ,μ-algebras are described.
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Minimal Nonzero L-Varieties of Vector Spaces Over the Field ℤ2 Algebra Logic (IF 0.5) Pub Date : 2023-04-20 A. V. Kislitsin
We provide a complete description of minimal nonzero L-varieties of multiplicative vector spaces over the field ℤ2.
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Intersection of Centralizers in a Partially Commutative Metabelian Group Algebra Logic (IF 0.5) Pub Date : 2023-04-19 E. I. Timoshenko
For a partially commutative metabelian group, necessary and sufficient conditions on a defining graph are found under which the intersection of centralizers of two distinct vertices of the graph and the commutator subgroup is trivial.
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A Criterion for Nonsolvability of a Finite Group and Recognition of Direct Squares of Simple Groups Algebra Logic (IF 0.5) Pub Date : 2023-04-05 Zh. Wang, A. V. Vasil’ev, M. A. Grechkoseeva, A. Kh. Zhurtov
The spectrum ω(G) of a finite group G is the set of orders of its elements. The following sufficient criterion of nonsolvability is proved: if, among the prime divisors of the order of a group G, there are four different primes such that ω(G) contains all their pairwise products but not a product of any three of these numbers, then G is nonsolvable. Using this result, we show that for q ⩾ 8 and q ≠
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Divisible Rigid Groups. Morley Rank Algebra Logic (IF 0.5) Pub Date : 2022-12-15 N. S. Romanovskii
Let G be a countable saturated model of the theory 𝔗m of divisible m-rigid groups. Fix the splitting G1G2 . . .Gm of a group G into a semidirect product of Abelian groups. With each tuple (n1, . . . , nm) of nonnegative integers we associate an ordinal α = ωm−1nm+ . . . + ωn2 + n1 and denote by G(α) the set \( {G}_1^{n_1}\times {G}_2^{n_2}\times \dots \times {G}_m^{n_m} \), which is definable over
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Minimal Generalized Computable Numberings and Families of Positive Preorders Algebra Logic (IF 0.5) Pub Date : 2022-12-15 F. Rakymzhankyzy, N. A. Bazhenov, A. A. Issakhov, B. S. Kalmurzayev
We study A-computable numberings for various natural classes of sets. For an arbitrary oracle A≥T0′, an example of an A-computable family S is constructed in which each A-computable numbering of S has a minimal cover, and at the same time, S does not satisfy the sufficient conditions for the existence of minimal covers specified in [Sib. Math. J., 43, No. 4, 616-622 (2002)]. It is proved that the family
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K-Completions of T0-Spaces Algebra Logic (IF 0.5) Pub Date : 2022-12-10 Yu. L. Ershov
For a wide category K, we introduce the notions of a K-precomplete map and of a K-subspace. Based on these, we create a uniform method for constructing K-completions of T0-spaces.
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Group and Algorithmic Properties of Generalized Baumslag–Solitar Groups Algebra Logic (IF 0.5) Pub Date : 2022-12-10 F. A. Dudkin
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Projections of Semilocal Rings Algebra Logic (IF 0.5) Pub Date : 2022-10-22 S. S. Korobkov
Associative rings are considered. By a lattice isomorphism (or projection) of a ring R onto a ring Rφ we mean an isomorphism φ of the subring lattice L(R) of a ring R onto the subring lattice L(Rφ) of a ring Rφ. Let Mn(GF(pk)) be the ring of all square matrices of order n over a finite field GF(pk), where n and k are natural numbers, p is a prime. A finite ring R with identity is called a semilocal
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Method of Verbal Operations and Automorphisms of the Category of Free Algebras Algebra Logic (IF 0.5) Pub Date : 2022-10-22 E. V. Aladova
Let an arbitrary variety of algebras and the category of all free finitely generated algebras in that variety be given. This paper is the second in a series of papers started in [Algebra and Logic, 61, No. 1, 1-15 (2022)] where we deal with automorphisms of the category of free finitely generated algebras. Here we describe in detail a method of verbal operations. The method provides a characterization
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Relatively Maximal Subgroups of Odd Index in Symmetric Groups Algebra Logic (IF 0.5) Pub Date : 2022-10-15 A. S. Vasil’ev, D. O. Revin
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Decomposability and Computability Algebra Logic (IF 0.5) Pub Date : 2022-10-15 B. Khoussainov, A. G. Melnikov
We present a new construction of indecomposable type 0 Abelian groups of rank 2. The new construction is used to study degree spectra of such groups. As a corollary, we obtain a new computability-theoretic proof showing that there exist continuum many nonisomorphic type 0 indecomposable Abelian groups of rank 2.
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Group Signature Formulas Constructed from Graphs Algebra Logic (IF 0.5) Pub Date : 2022-10-14 E. I. Timoshenko
Given a finite undirected graph Γ without loops, we define a sentence Φ(Γ) of group theory. A sequence of graphs Γi is used to obtain a sequence of sentences Φ(Γi). These are employed to determine the Γ-dimension of a group and to study properties of the dimension. Under certain restrictions on a group, the known centralizer dimension is the Γ-dimension for some sequence of graphs. We mostly focus
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Index Sets for Classes of Positive Preorders Algebra Logic (IF 0.5) Pub Date : 2022-08-06 B. S. Kalmurzayev, N. A. Bazhenov, M. A. Torebekova
We study the complexity of index sets with respect to a universal computable numbering of the family of all positive preorders. Let ≤c be computable reducibility on positive preorders. For an arbitrary positive preorder R such that the R-induced equivalence ∼R has infinitely many classes, the following results are obtained. The index set for preorders P with R ≤c P is \( {\sum}_3^0-\mathrm{complete}
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Automorphisms of the Category of Free Finitely Generated Algebras Algebra Logic (IF 0.5) Pub Date : 2022-08-06 E. V. Aladova
Let an arbitrary variety of algebras and the category of all free finitely generated algebras in that variety be given. In universal algebraic geometry over an arbitrary variety of algebras, the group of automorphisms of the category of free finitely generated algebras plays an important role. This paper is first in a series where we will deal with the group mentioned. Here we describe properties of
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Levi Classes of Quasivarieties of Nilpotent Groups of Exponent ps Algebra Logic (IF 0.5) Pub Date : 2022-08-06 V. V. Lodeishchikova, S. A. Shakhova
The Levi class L(M) generated by the class M of groups is the class of all groups in which the normal closure of every element belongs to M. It is proved that there exists a set of quasivarieties M of cardinality continuum such that \( L\left(\mathrm{M}\right)=L\left(q{H}_{p^s}\right) \), where \( q{H}_{p^s} \) is the quasivariety generated by the group \( {H}_{p^s} \), a free group of rank 2 in the
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Inner Constructivizability of Functional Structures Algebra Logic (IF 0.5) Pub Date : 2022-08-06 A. S. Burnistov, A. I. Stukachev
We construct and look at examples of (functional) structures the hereditarily finite superstructures over which have rank of inner constructivizability 0.
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Periodic Groups Saturated with Finite Simple Groups L4(q) Algebra Logic (IF 0.5) Pub Date : 2022-06-07 W. Guo, D. V. Lytkina, V. D. Mazurov
If M is a set of finite groups, then a group G is said to be saturated with the set M (saturated with groups in M) if every finite subgroup of G is contained in a subgroup isomorphic to some element of M. It is proved that a periodic group with locally finite centralizers of involutions, which is saturated with a set consisting of groups L4(q), where q is odd, is isomorphic to L4(F) for a suitable
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New Examples of Binary Lie Superalgebras and Algebras Algebra Logic (IF 0.5) Pub Date : 2022-05-23 A. N. Grishkov, I. P. Shestakov, M. N. Rasskazova
New constructions of prime binary Lie superalgebras are presented. Based on one of these, we construct the first example of a prime binary Lie algebra that is not a Mal’tsev algebra.
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The Homology of the Lamplighter Lie Algebra Algebra Logic (IF 0.5) Pub Date : 2022-05-16 Y. Félix, A. Murillo
It is proved that the associated Lie algebra of the Mal’tsev ℚ-completion of the lamplighter group is the pronilpotent completion of the lamplighter Lie algebra. It is also shown that the homology of this completed Lie algebra is of uncountable dimension in each degree.
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Fields of Algebraic Numbers Computable in Polynomial Time. II Algebra Logic (IF 0.5) Pub Date : 2022-05-06 P. E. Alaev, V. L. Selivanov
This paper is a continuation of [Algebra and Logic, 58, No. 6, 447-469 (2019)] where we constructed polynomial-time presentations for the field of complex algebraic numbers and for the ordered field of real algebraic numbers. Here we discuss other known natural presentations of such structures. It is shown that all these presentations are equivalent to each other and prove a theorem which explains
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Groups Saturated with Finite Frobenius Groups with Complements of Even Order Algebra Logic (IF 0.5) Pub Date : 2022-05-05 B. E. Durakov
We prove a theorem stating the following. Let G be a periodic group saturated with finite Frobenius groups with complements of even order, and let i be an involution of G. If, for some elements a, b ∈ G with the condition |a| · |b| > 4, all subgroups 〈a, bg〉, where g ∈ G, are finite, then G = A λ CG(i) is a Frobenius group with Abelian kernel A and complement CG(i) whose elementary Abelian subgroups
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Virtual Algebraic Isomorphisms between Predicate Calculi of Finite Rich Signatures Algebra Logic (IF 0.5) Pub Date : 2022-05-03 M. G. Peretyat’kin
It is proved that every two predicate calculi of finite rich signatures are algebraically virtually isomorphic, i.e., some of their Cartesian extensions are algebraically isomorphic. As an important application, it is stated that for predicate calculi in any two finite rich signatures, there exists a computable isomorphism between their Tarski–Lindenbaum algebras which preserves all model-theoretic
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Periodic Groups with Dense Spectrum Algebra Logic (IF 0.5) Pub Date : 2022-04-29 A. S. Mamontov
Presented by the Dissertation Council D 003.015.02
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Modal Bilattice Logic and its Extensions Algebra Logic (IF 0.5) Pub Date : 2022-04-29 S. O. Speranski
We consider the lattices of extensions of three logics: (1) modal bilattice logic; (2) full Belnap–Dunn bimodal logic; (3) classical bimodal logic. It is proved that these lattices are isomorphic to each other. Furthermore, the isomorphisms constructed preserve various nice properties, such as tabularity, pretabularity, decidability or Craig’s interpolation property.
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Complexity of the Problem of Being Equivalent to Horn Formulas Algebra Logic (IF 0.5) Pub Date : 2022-04-29 N. T. Kogabaev
We look at the complexity of the existence problem for a Horn sentence (identity, quasi-identity, ∀-sentence, ∃-sentence) equivalent to a given one. It is proved that if the signature contains at least one symbol of arity k ≥ 2, then each of the problems mentioned is an m-complete \( {\Sigma}_1^0 \) set.
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Abstract Relations Between Functional Clones Algebra Logic (IF 0.5) Pub Date : 2021-12-03 Pinus, A. G.
Functional clones on a set A are investigated at an abstract level, i.e., up to isomorphism of universal algebras 〈A; F〉, with their signature treated as an unindexed set. Abstract relations are introduced on a collection FA of all functional clones on A, and the question of their coincidence is discussed.
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T1-Separable Numberings of Subdirectly Indecomposable Algebras Algebra Logic (IF 0.5) Pub Date : 2021-12-03 Kasymov, N. Kh., Morozov, A. S., Khodzhamuratova, I. A.
We prove the existence of a natural subclass of subdirectly indecomposable algebras all of whose Hausdorff numberings are negative. We also construct a T1-separable nonnegative subdirectly indecomposable algebra with Artinian congruence lattice.
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Algebras of Distributions of Binary Isolating Formulas for Almost ω-Categorical Weakly o-Minimal Theories Algebra Logic (IF 0.5) Pub Date : 2021-12-03 Altayeva, A. B., Kulpeshov, B. Sh., Sudoplatov, S. V.
We describe distribution algebras of binary isolating formulas over 1-type for almost ω-categorical weakly o-minimal theories. It is proved that an isomorphism of these algebras for two 1-types is characterized by the coincidence of binary convexity ranks, as well as by the simultaneous fulfillment of isolation, quasirationality or irrationality of the two types. A criterion is established for an algebra
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The Category of Equivalence Relations Algebra Logic (IF 0.5) Pub Date : 2021-12-03 V. Delle Rose, L. San Mauro, A. Sorbi
We make some beginning observations about the category 𝔼q of equivalence relations on the set of natural numbers, where a morphism between two equivalence relations R and S is a mapping from the set of R-equivalence classes to that of S-equivalence classes, which is induced by a computable function. We also consider some full subcategories of 𝔼q, such as the category \( \mathbbm{E}\mathrm{q}\lef