Finite groups with five relative commutativity degrees

TL;DR

This paper classifies all finite groups that have exactly five relative commutativity degrees and addresses a conjecture regarding the minimum number of such degrees in finite groups.

Contribution

It provides a complete classification of finite groups with five relative commutativity degrees and offers partial progress on a conjecture about their lower bounds.

Findings

Classification of all finite groups with five relative commutativity degrees

Partial validation of a conjecture on the lower bound of relative commutativity degrees

Insight into the structure of finite groups based on their commutativity properties

Abstract

We classify all finite groups with five relative commutativity degrees. Also, we give a partial answer to our previous conjecture on a lower bound of the number of relative commutativity degrees of finite groups.