A characterization of generalized quaternion 2-groups

TL;DR

This paper characterizes generalized quaternion 2-groups by examining their posets of cyclic subgroups, providing a structural understanding of these groups.

Contribution

It introduces a new characterization of generalized quaternion 2-groups based on their cyclic subgroup posets, advancing group theory knowledge.

Findings

Provides a unique characterization of generalized quaternion 2-groups

Uses posets of cyclic subgroups as a key tool

Enhances understanding of group structure

Abstract

The goal of this note is to give a characterization of generalized quaternion $2$-groups by using their posets of cyclic subgroups.