On the number of prime divisors of character degrees and conjugacy classes of a finite group
- Resource Type
- article
- Authors
- Yang, Yong
- Source
- Comptes Rendus. Mathématique, Vol 360, Iss G6, Pp 583-588 (2022)
- Subject
- Mathematics
QA1-939
- Language
- English
French
- ISSN
- 1778-3569
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.