Abelian subgroups, nilpotent subgroups, and the largest character degree of a finite group

JOURNAL OF ALGEBRA

卷:551

Article

Nguyen Ngoc Hung¹  Yang, Yong² 

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

[2] Texas State Univ, Dept Math, San Marcos, TX 78666 USA

关键词: Finite groups;    Abelian subgroups;    Nilpotent subgroups;    Character degrees;    Largest character degree;    Gluck's conjecture;   

DOI  :  10.1016/j.jalgebra.2019.09.010

来源: Elsevier

【 摘 要 】

Let H be an abelian subgroup of a finite group G and pi the set of prime divisors of vertical bar H vertical bar. We prove that vertical bar HO pi(G)/O-pi(G)vertical bar is bounded above by the largest character degree of G. A similar result is obtained when H is nilpotent. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free