Height-zero characters and normal subgroups in p-solvable groups

JOURNAL OF ALGEBRA

卷:399

Article

Laradji, A.

关键词: Finite groups;    Solvable groups;    Ordinary characters;    p-Blocks;   

DOI  :  10.1016/j.jalgebra.2013.10.014

来源: Elsevier

【 摘 要 】

Fix a prime number p, and let N be a normal subgroup of a finite p-solvable group G. Let b be a p-block of N and suppose B is a p-block of G covering b. Let D be a defect group for the Fong-Reynolds correspondent of B with respect to b and let (B) over cap be the unique p-block of NNG(D) having defect group D and inducing B. Suppose, further, that mu is an element of lrr(b), and let Irr(0)(B vertical bar mu) be the set of irreducible characters in B of height zero that lie over mu. We show that the number of characters in Irr(0)(B vertical bar mu) is equal to the number of characters in boolean OR(t) Irr(0)((B) over cap vertical bar mu(t)), where t runs through the inertial group T of b in G. This result generalizes a theorem of T. Okuyama and M. Wajima, which confirms the Alperin-McKay conjecture for p-solvable groups. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free