2-Blocks with minimal nonabelian defect groups

被引：16

作者：

Sambale, Benjamin ^{[1
]}

机构：

[1] Univ Jena, Math Inst, D-07743 Jena, Germany

来源：

JOURNAL OF ALGEBRA | 2011年 / 337卷 / 01期

关键词：

Blocks of finite groups; Minimal nonabelian defect groups; Alperin's conjecture; Dade's conjecture; INERTIAL INDEX 2; IRREDUCIBLE CHARACTERS; PERFECT ISOMETRIES; P-BLOCKS; SECTIONS;

D O I：

10.1016/j.jalgebra.2011.02.006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study numerical invariants of 2-blocks with minimal non-abelian defect groups. These groups were classified by Redei (see Redei, 1947 [41]). If the defect group is also metacyclic, then the block invariants are known (see Sambale 1431). In the remaining cases there are only two (infinite) families of 'interesting' defect groups. In all other cases the blocks are nilpotent. We prove Brauer's k(B)-conjecture and Olsson's conjecture for all 2-blocks with minimal nonabelian defect groups. For one of the two families we also show that Alperin's weight conjecture and Dade's conjecture are satisfied. This paper is a part of the author's PhD thesis. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：261 / 284

页数：24

共 46 条

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