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arXiv · 2308.13948

Semi-Generalized Bassian Groups

Andrey R. Chekhlov·Peter V. Danchev·Patrick W. Keef
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Abstract

As a common non-trivial generalization of the concept of a proper generalized Bassian group, we introduce the notion of a semi-generalized Bassian group and initiate its comprehensive investigation. Precisely, we give a satisfactory characterization of these groups by showing in the cases of p-torsion groups, torsion-free groups and splitting mixed groups their complete description. Moreover, we classify the groups with the clearly related property that every subgroup is essential in a direct summand of the whole group.

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Andrey R. Chekhlov, Peter V. Danchev, Patrick W. Keef. 2023-08-26. Semi-Generalized Bassian Groups. https://arxiv.org/abs/2308.13948

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