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Algebra
On the number of prime divisors of character degrees and conjugacy classes of a finite group
Yong Yang1, 2 
1 Department of Mathematics, Texas State University, San Marcos, TX 78666, USA
2 Three Gorges Mathematical Research Center, College of Science, China Three Gorges University, Yichang, Hubei 443002, China
Comptes Rendus. Mathématique, Volume 360 (2022), 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.

Received:
Accepted:
Published online:
DOI: 10.5802/crmath.301
Classification: 20C15, 20C20

Yong Yang 1, 2

1 Department of Mathematics, Texas State University, San Marcos, TX 78666, USA
2 Three Gorges Mathematical Research Center, College of Science, China Three Gorges University, Yichang, Hubei 443002, China
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Yong Yang. On the number of prime divisors of character degrees and conjugacy classes of a finite group. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 583-588. doi : 10.5802/crmath.301. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.301/

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