Semi-Generalized Bassian Groups
Andrey R. Chekhlov, Peter V. Danchev, and Patrick W. Keef

TL;DR
This paper introduces semi-generalized Bassian groups, providing their complete characterization in various cases and exploring related subgroup properties, advancing the understanding of this new class of groups.
Contribution
It defines semi-generalized Bassian groups and offers a comprehensive classification in p-torsion, torsion-free, and splitting mixed groups, expanding group theory knowledge.
Findings
Complete characterization of semi-generalized Bassian groups in specific cases
Classification of groups with every subgroup essential in a direct summand
Extension of Bassian group concepts to broader classes
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.
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Taxonomy
TopicsFuzzy and Soft Set Theory
