Existence criterion for Hall subgroups of finite groups

TL;DR

This paper establishes a criterion based on composition series to determine the existence of Hall subgroups within finite groups, advancing the understanding of subgroup structure.

Contribution

It introduces a new existence criterion for Hall subgroups using composition series, providing a novel theoretical tool.

Findings

Provides a criterion for Hall subgroup existence

Connects subgroup existence to composition series

Enhances subgroup classification methods

Abstract

In the paper we obtain an existence criterion for Hall subgroups of finite groups in terms of a composition series.