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 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.
Authors
- Peter Danchev (ORCID: https://orcid.org/0000-0002-2016-2336)
- A. R. Chekhlov (ORCID: https://orcid.org/0000-0002-9078-128X)
- Patrick W. Keef (ORCID: https://orcid.org/0000-0003-4983-2273)
Institutions
- Whitman College (US)
- National Research Tomsk State University (RU)
- Bulgarian Academy of Sciences (BG)
- Institute of Mathematics and Informatics (BG)
Publication Details
- Journal
- Journal of Group Theory
- Published
- 2024-09-23
- DOI
- https://doi.org/10.1515/jgth-2023-0229
- Citations
- 2
- Primary Topic
- Advanced Algebra and Logic
- Type
- article
- Field-Weighted Citation Impact
- 0.72
Funders
- Junta de Andalucía
- Ministry of Science and Higher Education of the Russian Federation