In:
Mathematical Proceedings of the Cambridge Philosophical Society, Cambridge University Press (CUP), Vol. 156, No. 3 ( 2014-05), p. 555-570
Abstract:
We 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.
Type of Medium:
Online Resource
ISSN:
0305-0041
,
1469-8064
DOI:
10.1017/S0305004114000103
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
2014
detail.hit.zdb_id:
1483586-1
detail.hit.zdb_id:
209201-3
SSG:
17,1
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