A note on a metric associated to certain finite groups

TL;DR

This paper introduces a new metric on specific finite groups, leading to a class where element orders satisfy a notable inequality, extending previous work on the CP_2 class.

Contribution

It proposes a novel metric on finite groups and extends the class of groups with particular order inequalities beyond CP_2.

Findings

Defined a new metric on certain finite groups

Identified a new class of groups with order inequalities

Extended previous class CP_2 to a broader class

Abstract

In this short note we introduce a new metric on certain finite groups. It leads to a class of groups for which the element orders satisfy an interesting inequality. This extends the class CP_2 studied in our previous paper [16].