Blocks with the hyperfocal subgroup Z2n X Z2n

JOURNAL OF ALGEBRA

卷:518

Article

Hu, Xueqin¹  Zhou, Yuanyang¹ 

[1] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China

关键词: Hyperfocal subgroup;    Brauer character;    Lower defect group;    Brauer category;   

DOI  :  10.1016/j.jalgebra.2018.09.039

来源: Elsevier

【 摘 要 】

In this paper, we calculate the numbers of irreducible ordinary characters and irreducible Brauer characters in a block of a finite group G, whose associated fusion system over a 2-subgroup P of G (which is a defect group of the block) has hyperfocal subgroup Z(2)(n) x Z(2)(n) for a positive integer number n, when the block is controlled by the normalizer N-G(P) and the hyperfocal subgroup is contained in the center of P, or when the block is not controlled by N-G(P) and the hyperfocal subgroup is contained in the center of the unique essential subgroup in the fusion system and has order at most 16. In particular, Alperin's weight conjecture holds in the considered cases. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free