Enumeration of conjugacy classes in affine groups

DOI10.2140/ANT.2024.18.1189arXiv2112.15219OpenAlexW4396559815MaRDI QIDQ6387126

Publication date: 30 December 2021

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 non-coprime k(GV) problem of Brauer.

Full work available at URL: https://doi.org/10.2140/ant.2024.18.1189

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Conjugacy classes for groups (20E45) Linear algebraic groups over finite fields (20G40) Ordinary representations and characters (20C15) Modular representations and characters (20C20)

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