Author:
KOSHITANI SHIGEO,KÜLSHAMMER BURKHARD,SAMBALE BENJAMIN
Abstract
AbstractWe give a lower bound on the Loewy length of a p-block of a finite group in terms of its defect. We then discuss blocks with small Loewy length. Since blocks with Loewy length at most 3 are known, we focus on blocks of Loewy length 4 and provide a relatively short list of possible defect groups. It turns out that p-solvable groups can only admit blocks of Loewy length 4 if p=2. However, we find (principal) blocks of simple groups with Loewy length 4 and defect 1 for all p ≡ 1 (mod 3). We also consider sporadic, symmetric and simple groups of Lie type in defining characteristic. Finally, we give stronger conditions on the Loewy length of a block with cyclic defect group in terms of its Brauer tree.
Publisher
Cambridge University Press (CUP)
Reference48 articles.
1. Fusion systems on metacyclic 2-groups;Sambale;Osaka J. Math.,2012
2. Nilpotent blocks and their source algebras
3. On lower bounds for the radical of a block ideal in a finite p-solvable group
4. A lower bound for the representation dimension of $${kC_p^n}$$
5. The GAP Group GAP – Groups, Algorithms and Programming, Version 4.6.4 (2013) (http://www.gap-system.org).
Cited by
13 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献