Semi-generalized Bassian groups

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...

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Bibliographic Details
Published inJournal of group theory
Main Authors Chekhlov, Andrey R., Danchev, Peter V., Keef, Patrick W.
Format Journal Article
LanguageEnglish
Published 24.09.2024
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Summary: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 -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.
ISSN:1433-5883
1435-4446
DOI:10.1515/jgth-2023-0229