Lower bounds on the maximum dimension of a simple module in\n characteristic p

2020/08/08 by Geoffrey R. Robinson, Robinson, Geoffrey R.
Mathematics · #20C20 #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2008.03490

openalex publication_date 2020/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain lower bounds for the maximum dimension of a simple FG-module, where\nG is a finite group and F is an algebraically closed field of characteristic p.\nThe bounds are described in terms of properties of p-subgroups of G. When p is\n2 or p is a Mersenne prime, the bounds take a different form, due to exceptions\nwhich arise for such primes.\n

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