Finite groups determined by an inequality of the orders of their normal subgroups

TL;DR

This paper introduces a new class of finite groups characterized by an inequality involving the orders of their normal subgroups, linking group theory with certain arithmetic properties of natural numbers.

Contribution

It defines and investigates a novel class of finite groups based on inequalities of normal subgroup orders, connecting group structure with number-theoretic concepts.

Findings

Characterization of the new class of finite groups

Connections established between group properties and arithmetic classes

Potential classification results for groups satisfying the inequality

Abstract

In this article we introduce and study a class of finite groups for which the orders of normal subgroups satisfy a certain inequality. It is closely connected to some well-known arithmetic classes of natural numbers.