On finite groups factorised by submodular subgroups

TL;DR

This paper studies the structure of finite groups that can be broken down into factors with submodular subgroups, providing a new approach to understanding groups with supersolvable submodular factors.

Contribution

It introduces a general method for describing finite groups factorised by supersolvable submodular subgroups, expanding the understanding of their structure.

Findings

Characterization of finite groups with submodular primary subgroups

A new approach to describing groups with supersolvable submodular factors

Insights into the subgroup chain structures within factorised groups

Abstract

A subgroup $H$ of a finite group $G$ is submodular in $G$ if there is a subgroup chain $H=H_0\leq\ldots\leq H_i\leq H_{i+1}\leq \ldots \leq H_n=G$ such that $H_i$ is a modular subgroup of $H_{i+1}$ for every $i$. We investigate finite factorised groups with submodular primary (cyclic primary) subgroups in factors. We indicate a general approach to the description of finite groups factorised by supersolvable submodular subgroups.