Algèbre
On the number of prime divisors of character degrees and conjugacy classes of a finite group
Yang, Yong1, 2
1 Three Gorges Mathematical Research Center, College of Science, China Three Gorges University, Yichang, Hubei 443002, China
2 Department of Mathematics, Texas State University, San Marcos, TX 78666, USA
Comptes Rendus. Mathématique, Tome 360 (2022) no. G6, pp. 583-588.

A result of Gluck is that any finite group G has an abelian subgroup A such that |G:A| is bounded by a polynomial function of the largest irreducible character degree of G. Moretó 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 Moretó 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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DOI : 10.5802/crmath.301
Classification : 20C15, 20C20
Yang, Yong 1, 2

1 Three Gorges Mathematical Research Center, College of Science, China Three Gorges University, Yichang, Hubei 443002, China
2 Department of Mathematics, Texas State University, San Marcos, TX 78666, USA 
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     title = {On the number of prime divisors of character degrees and conjugacy classes of a finite group},
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Yang, Yong. On the number of prime divisors of character degrees and conjugacy classes of a finite group. Comptes Rendus. Mathématique, Tome 360 (2022) no. G6, pp. 583-588. doi : 10.5802/crmath.301. https://www.numdam.org/articles/10.5802/crmath.301/

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