Bounding the even abelian composition factors in finite linear groups

Gutierrez, Awildo; Huang, Yuqiao; Peckham, Duncan; Yang, Yong

doi:10.2140/involve.2023.16.265

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Bounding the even abelian composition factors in finite linear groups

Awildo Gutierrez, Yuqiao Huang, Duncan Peckham and Yong Yang

Vol. 16 (2023), No. 2, 265–276

DOI: 10.2140/involve.2023.16.265

Abstract

We study the product of the orders of the even abelian composition factors of a finite linear group. We show that if $G$ is a finite group acting faithfully and completely reducibly on a vector space $V$ , then the product of the orders of the even abelian composition factors of $G$ is bounded above by a function of $| V |$ .

Keywords

linear groups, composition factors

Mathematical Subject Classification

Primary: 20C15, 20C20

Milestones

Received: 10 October 2021

Revised: 12 May 2022

Accepted: 18 May 2022

Published: 26 May 2023

Communicated by Kenneth S. Berenhaut

Authors

Awildo Gutierrez
Department of Mathematics and Statistics Hamilton College Clinton, NY United States

Yuqiao Huang
Department of Mathematics University of Rochester Rochester, NY United States

Duncan Peckham
Department of Mathematics and Statistics Boston University Boston, MA United States

Yong Yang
Department of Mathematics Texas State University San Marcos, TX United States

Vol. 16, No. 2, 2023