Semi-generalized Bassian groups
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Andrey R. Chekhlov
and
Patrick W. Keef
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 đť‘ť-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.
Award Identifier / Grant number: 075-02-2024-1437
Funding source: Junta de AndalucĂa
Award Identifier / Grant number: FQM 264
Funding statement: The work of the first-named author A. R. Chekhlov was supported by the Ministry of Science and Higher Education of Russia (agreement No. 075-02-2024-1437). The work of the second-named author P. V. Danchev was partially supported by the Junta de AndalucĂa under Grant FQM 264.
Acknowledgements
The authors are very thankful to the handling editor, Prof. Anton Klyachko, to the managing editors, Profs. Tim Burness and Chris Parker, as well as to the two expert referees, for their numerous valuable suggestions that improved the article’s shape significantly.
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Communicated by: Anton Klyachko
References
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© 2024 Walter de Gruyter GmbH, Berlin/Boston
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Articles in the same Issue
- Frontmatter
- Finite simple permutation groups acting with fixity 4
- Flag-transitive 2-designs with prime-square or prime-cube block length
- Monster embeddings of certain 3-transposition groups via Majorana representations
- Finite groups with a small proportion of vanishing elements
- On 𝜎-permutable subgroups of 𝜎-soluble finite groups
- Semi-generalized Bassian groups
- Absolute ideals of almost completely decomposable abelian groups
- Orbit-blocking words and the average-case complexity of Whitehead’s problem in the free group of rank 2
- Subgroups of even Artin groups of FC type
- On decidability of the product of subgroups membership problem for nilpotent groups
- On generalized concise words
- Corrigendum to Centralizers of subsystems of fusion systems [J.~Group Theory 18 (2015), 393--405]
