Finite groups determined by an inequality of the orders of their elements

TL;DR

This paper introduces a new class of finite groups characterized by an inequality involving element orders, expanding understanding of group classifications within existing well-known categories.

Contribution

It defines and characterizes a novel class of finite groups based on element order inequalities, enriching the taxonomy of finite group structures.

Findings

Identifies a new class of finite groups based on element order inequalities

Shows this class is contained within some well-known finite groups

Provides characterization criteria for these groups

Abstract

In this note we introduce and characterize a class of finite groups for which the element orders satisfy a certain inequality. This is contained in some well-known classes of finite groups.