The abelian group G is co-Bassian if for all subgroups \(N\subseteq G\), if \(\phi : G\rightarrow G/N\) is an injective homomorphism, then \(\phi (G)=G/N\). And G is generalized co-Bassian if for all subgroups \(N\subseteq G\), if \(\phi : G\rightarrow G/N\) is an injective homomorphism, then \(\phi (G)\) is a summand of G/N. The co-Bassian and generalized co-Bassian groups are completely characterized. These notions are dual to the concepts of Bassian and generalized Bassian groups that were studied in papers by Chekhlov, Danchev, and Goldsmith (2021 and 2022), and later by Danchev and Keef (2023).

阿贝尔群G是共巴斯群，如果对于所有子群\(N\subseteq G\)，如果\(\phi : G\rightarrow G/N\)是单射同态，则\(\phi (G)=G /N\)。如果对于所有子群\(N\subseteq G\)，如果\(\phi : G\rightarrow G/N\)是单射同态，则G是广义 co-Bassian ，则\(\phi (G)\)是G / N的被加数。共巴塞亚群和广义共巴塞亚群得到了完整的表征。这些概念与契赫洛夫、丹切夫和戈德史密斯（2021 年和 2022 年）以及后来丹切夫和基夫（2023 年）在论文中研究的巴斯群和广义巴斯群的概念是双重的。