An algorithm for determining the simplicity of a modular group representation*

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Abstract

Let G be a finite group an F and arbitrary splitting field for G. Using the Amitsur-Levitzki theorem on the polynomial identities satisfied by a matrix ring over a commutative ring an algorithm is given for finding the minimal dimension t for which there is a simple t-dimensional FG-submodule U in a faithful FG-module M of dimension n <∞. As a corollary a new criterion is obtained for checking the simplicity of a finite-dimensional group representation.

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*

This paper is dedicated to Professor B. Huppert on the occasio of his 60th birthday.