Article ID Journal Published Year Pages File Type
8904918 Advances in Mathematics 2018 11 Pages PDF
Abstract
Let G be a finite group and Irr(G) the set of irreducible complex characters of G. Let ep(G) be the largest integer such that pep(G) divides χ(1) for some χ∈Irr(G). We show that |G:F(G)|p≤pkep(G) for a constant k. This settles a conjecture of A. Moretó [13, Conjecture 4]. We also study the related problems of the p-parts of conjugacy class sizes of finite groups.
Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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