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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
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