Blocks with the hyperfocal subgroup Z_2ⁿ× Z_2ⁿ

2017/09/18 by Xueqin Hu, Hu, Xueqin, Yuanyang Zhou +1
Chemistry · Mathematics · #Algebraic Geometry and Number Theory #Crystal structures of chemical compounds #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.1709.05983

openalex publication_date 2017/09/18 · arxiv created 2018/08/29 · arxiv updated 2018/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 the hyperfocal subgroup \mathbb Z_2ⁿ× \mathbb Z_2ⁿ for some n≥ 2, 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. In particular, Alperin's weight conjecture holds in the considered cases.

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• p-Blocks Relative to a Character of a Normal Subgroup
• Blocks with defect group D_2ⁿ x C_2^m
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