The average character degree and an improvement of the It(o)over-cap-Michler theorem

JOURNAL OF ALGEBRA

卷:550

Article

Nguyen Ngoc Hung¹  Pham Huu Tiep² 

[1] Univ Akron, Dept Math, Akron, OH 44325 USA

[2] Rutgers State Univ, Dept Math, Piscataway, NJ 08854 USA

关键词: Finite groups;    Simple groups;    Character degrees;    Normal subgroups;    Sylow subgroups;    It(o)over-cap-Michler theorem;   

DOI  :  10.1016/j.jalgebra.2019.12.022

来源: Elsevier

【 摘 要 】

The classical It (o) over cap -Michler theorem states that the degree of every ordinary irreducible character of a finite group G is coprime to a prime p if and only if the Sylow p-subgroups of G are abelian and normal. In an earlier paper [8], we used the notion of average character degree to prove an improvement of this theorem for the prime p = 2. In this follow-up paper, we obtain a full improvement for all primes. Published by Elsevier Inc.

【 授权许可】

Free