The Fitting height is bounded by a function of the exponent

TL;DR

This paper establishes a new upper bound for the Fitting height of finite solvable groups based on their exponent, improving upon previous bounds and enhancing understanding of group structure.

Contribution

The paper introduces a significantly improved upper bound for the Fitting height in terms of the group's exponent, advancing the theoretical understanding of solvable groups.

Findings

Derived a new upper bound for Fitting height based on group exponent

Improved upon earlier bounds by Shalev

Provides insights into the structure of finite solvable groups

Abstract

Every finite solvable group $G$ has a normal series with nilpotent factors. The smallest possible number of factors in such a series is called the Fitting height $h(G)$. In the present paper, we derive an upper bound for $h(G)$ in terms of the exponent of $G$. Our bound constitutes a considerable improvement of an earlier bound obtained by Shalev.