A generalization of 2-Baer groups

TL;DR

This paper explores generalized 2-Baer groups, focusing on their structure, nilpotency, and examples of finite p-groups that fit this classification, extending the understanding of subgroup normality conditions.

Contribution

It introduces and analyzes generalized 2-Baer groups, providing new structural results, nilpotency insights, and explicit examples of finite p-groups within this class.

Findings

Structure results for generalized T_2-groups

Investigation of their nilpotency class

Construction of finite p-group examples

Abstract

A group in which all cyclic subgroups are 2-subnormal is called a 2-Baer group. The topic of this paper are generalized 2-Baer groups, i.e. groups in which the non-2-subnormal cyclic subgroups generate a proper subgroup of the group. If this subgroup is non-trivial, the group is called a generalized T_2-group. In particular, we provide structure results for such groups, investigate their nilpotency class and construct examples of finite p-groups which are generalized T_2-groups.