On the Fitting length of finite soluble groups I

TL;DR

This paper investigates upper bounds for the Fitting length of finite soluble groups based on the Fitting lengths of specific Hall subgroups that factorize the group, providing insights into the structure of such groups.

Contribution

It introduces new bounds for the Fitting length of finite soluble groups using the Fitting lengths of three Hall subgroups with a particular factorization.

Findings

Derived upper bounds for Fitting length based on Hall subgroups

Established relationships between subgroup Fitting lengths and the whole group

Provided structural insights into soluble groups with specific factorizations

Abstract

Let $G$ be a finite soluble group and $h(G)$ its Fitting length. The aim of this paper is to give certain upper bounds for $h(G)$ as functions of the Fitting length of at least three Hall subgroups of $G$ which factorize $G$ in a particular way.