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Brauer characters of prime power degrees and conjugacy classes of prime power lengths

by Pham Huu Tiep, Wolfgang Willems.

Series: 2008-04, Preprints

20C20 Modular representations and characters
20E34 General structure theorems
20D06 Simple groups: alternating groups and groups of Lie type
20D08 Simple groups: sporadic groups

We classify all finite non-abelian simple groups for which the degrees of irreducible Brauer characters are powers of a fixed prime.
Analogously we classify all finite groups for which the
lengths of regular conjugacy classes are powers of a fixed prime.