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Enumeration of conjugacy classes in affine groups

Jason Fulman and Robert M. Guralnick
Vol. 18 (2024), No. 6, 1189–1219
DOI: 10.2140/ant.2024.18.1189
Abstract

We study the conjugacy classes of the classical affine groups. We derive generating functions for the number of classes analogous to formulas of Wall and the authors for the classical groups. We use these to get good upper bounds for the number of classes. These naturally come up as difficult cases in the study of the noncoprime k(GV ) problem of Brauer.

Dedicated to Pham Huu Tiep on the occasion of his 60th birthday
Keywords
affine groups, number of conjugacy classes, generating function
Mathematical Subject Classification
Primary: 05A15, 20C99
Milestones
Received: 25 January 2022
Revised: 10 January 2023
Accepted: 3 September 2023
Published: 30 April 2024
Authors
Jason Fulman
Department of Mathematics
University of Southern California
Los Angeles
United States
Robert M. Guralnick
Department of Mathematics
University of Southern California
Los Angeles
United States
© 2024 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY).

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