Work

Semi-generalized Bassian groups

Year: 2024

Type: article

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.

Source: Journal of Group Theory

DOI: 10.1515/jgth-2023-0229

Authors: Andrey R. Chekhlov, Peter V. Danchev, Patrick W. Keef

Institutions: National Research Tomsk State University, Bulgarian Academy of Sciences, Institute of Mathematics and Informatics, Whitman College

Language: English

Topic: Rings, Modules, and Algebras

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Bulgarian National Science Fund, Junta de Andalucía, Ministry of Science and Higher Education of the Russian Federation

Awards: G1737173237, G6288273012