Semi-Generalized co-Bassian Groups

TL;DR

This paper introduces semi-generalized co-Bassian groups, extending the concept of generalized co-Bassian groups, and provides a complete characterization for p-torsion and finite torsion-free rank groups, revealing deep structural insights.

Contribution

It defines semi-generalized co-Bassian groups and characterizes them for specific classes, linking them to generalized co-Bassian groups and torsion properties.

Findings

Characterization of semi-generalized co-Bassian groups for p-torsion groups.

Complete description of these groups in terms of generalized finite p-ranks.

Connection between semi-generalized and generalized co-Bassian groups for p-primary cases.

Abstract

As a common non-trivial generalization of the notion of a generalized co-Bassian group, recently defined by the third author, we introduce the notion of a semi-generalized co-Bassian group and initiate its comprehensive study. Specifically, we give a complete characterization of these groups in the cases of p-torsion groups and groups of finite torsion-free rank by showing that these groups can be completely determined in terms of generalized finite p-ranks and also depends on their quotients modulo the maximal torsion subgroup. Surprisingly, for p-primary groups, the concept of a semi-generalized co-Bassian group is closely related to that of a generalized co-Bassian group.