On abelian subgroups of finite groups

TL;DR

This paper investigates the properties of abelian subgroups with small index in finite groups, focusing on the relationship between subgroup index and centralizer index to understand their structure.

Contribution

It introduces a new perspective on abelian subgroups by analyzing the product of their index and the index of their centralizer, extending previous studies.

Findings

Characterization of abelian subgroups with small index

Relationships between subgroup index and centralizer index

Insights into the structure of finite groups with such subgroups

Abstract

We consider abelain subgroups of small index in finite groups. More generally, we consider subgroups such that the product of their index by the index of their centralizer is small.