Finitely generated metabelian groups arising from integer polynomials

References

[1] R. Bieri and R. Strebel, Valuations and finitely presented metabelian groups, Proc. Lond. Math. Soc. (3) 41 (1980), no. 3, 439–464. 10.1112/plms/s3-41.3.439Search in Google Scholar

[2] P. Hall, Finiteness conditions for soluble groups, Proc. Lond. Math. Soc. (3) 4 (1954), 419–436. 10.1112/plms/s3-4.1.419Search in Google Scholar

[3] P. Hall, On the finiteness of certain soluble groups, Proc. Lond. Math. Soc. (3) 9 (1959), 595–622. 10.1112/plms/s3-9.4.595Search in Google Scholar

[4] P. Hall, The Frattini subgroups of finitely generated groups, Proc. Lond. Math. Soc. (3) 11 (1961), 327–352. 10.1112/plms/s3-11.1.327Search in Google Scholar

[5] B. Hartley, The residual nilpotence of wreath products, Proc. Lond. Math. Soc. (3) 20 (1970), 365–392. 10.1112/plms/s3-20.3.365Search in Google Scholar

[6] T. M. Lam, Lectures on Rings and Modules, Springer, Berlin, 1999. Search in Google Scholar

[7] J. C. Lennox and D. J. S. Robinson, The Theory of Infinite Soluble Groups, Oxford Math. Monogr., Oxford University, Oxford, 2004. 10.1093/acprof:oso/9780198507284.001.0001Search in Google Scholar

[8] H. G. Liu, J. P. Zhang, X. Z. Xu and J. Liao, A note on polycyclic groups, Acta Math. Sinica (Chinese Ser.) 66 (2023), no. 3, 399–404. Search in Google Scholar

[9] X. Luo, H. Liu, X. Xu and J. Liao, On the residual finiteness of a class of polycyclic groups, Chinese Ann. Math. Ser. A 42 (2021), no. 1, 33–46. Search in Google Scholar

[10] D. J. S. Robinson, A Course in the Theory of Groups, 2nd ed., Grad. Texts in Math. 80, Springer, New York, 1996. 10.1007/978-1-4419-8594-1Search in Google Scholar

[11] R. Y. Sharp, Steps in Commutative Algebra, 2nd ed., London Math. Soc. Stud. Texts 51, Cambridge University, Cambridge, 2000. Search in Google Scholar