p-Parts of Brauer character degrees

JOURNAL OF ALGEBRA

卷:403

Article

Navarro, Gabriel¹  Pham Huu Tiep²  Tong-Viet, Hung P.³ 

[1] Univ Valencia, Dept Algebra, E-46100 Valencia, Spain

[2] Univ Arizona, Dept Math, Tucson, AZ 85721 USA

[3] Univ KwaZulu Natal, Sch Math Stat & Comp Sci, ZA-3209 Pietermaritzburg, South Africa

关键词: Brauer characters;    Solvable groups;   

DOI  :  10.1016/j.jalgebra.2014.01.022

来源: Elsevier

【 摘 要 】

Let G be a finite group and let p be an odd prime. Under certain conditions on the p-parts of the degrees of its irreducible p-Brauer characters, we prove the solvability of G. As a consequence, we answer a question proposed by B. Huppert in 1991: If G has exactly two distinct irreducible p-Brauer character degrees, then is G solvable? We also determine the structure of non-solvable groups with exactly two irreducible 2-Brauer character degrees. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free