On the odd order composition factors of finite linear groups

TL;DR

This paper investigates the structure of finite linear groups by analyzing the product of the orders of their odd order composition factors, providing bounds and generalizations of existing results.

Contribution

It generalizes a known result on solvable linear groups of odd order and establishes bounds for the product of odd order composition factors in finite linear groups.

Findings

Generalized Manz and Wolf's result on solvable groups

Established bounds for the product of odd order composition factors

Enhanced understanding of the structure of finite linear groups

Abstract

In this paper, we study the product of orders of composition factors of odd order in a composition series of a finite linear group. First we generalize a result by Manz and Wolf about the order of solvable linear groups of odd order. Then we use this result to find bounds for the product of orders of composition factors of odd order in a composition series of a finite linear group.