科研之友
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摘要
A result of Gluck is that any finite group G has an abelian subgroup A such that vertical bar G : A vertical bar is bounded by a polynomial function of the largest irreducible character degree of G. Moreto presented a variation of this result that looks at the number of prime factors of the irreducible character degrees and obtained an almost quadratic bound. The author improved the result of Moreto to almost linear. In this note, we further improve the bound, and also study the related problem on conjugacy class sizes.
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