Finite groups with many p-regular conjugacy classes

2023/05/22 by C. A. Schroeder, Schroeder, Christopher A. · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #20D20 (Secondary) #20E45 (Primary) 20D10 #Chromatin Remodeling and Cancer #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2305.12905

openalex publication_date 2023/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finite group and let p be a prime. In this paper, we study the structure of finite groups with a large number of p-regular conjugacy classes or, equivalently, a large number of irreducible p-modular representations. We prove sharp lower bounds for this number in terms of p and the p'-part of the order of G which ensure that G is p-solvable. A bound for the p-length is obtained which is sharp for odd primes p. We also prove a new best possible criterion for the existence of a normal Sylow p-subgroup in terms of these quantities.

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