Semi-Generalized Bassian Groups

2023/08/26 by A. R. Chekhlov, Peter Danchev, Chekhlov, Andrey R. +3
Decision Sciences · #20K10 #20K20 #20K30 #FOS: Mathematics #Fuzzy and Soft Set Theory #Group Theory (math.GR) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2308.13948

openalex publication_date 2023/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

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• Supper Bassian and Nearly Generalized Bassian Abelian Groups
• Generalized Bassian and other Mixed Abelian Groups with Bounded p-Torsion
• Generalizations of the Bassian and co-Bassian Properties for Abelian Groups
• Two Generalizations of co-Hopfian Abelian Groups