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arXiv · 2008.03490

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

Geoffrey R. Robinson
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Abstract

We obtain lower bounds for the maximum dimension of a simple FG-module, where G is a finite group and F is an algebraically closed field of characteristic p. The bounds are described in terms of properties of p-subgroups of G. When p is 2 or p is a Mersenne prime, the bounds take a different form, due to exceptions which arise for such primes.

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Geoffrey R. Robinson. 2020-08-08. Lower bounds on the maximum dimension of a simple module in characteristic p. https://arxiv.org/abs/2008.03490

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