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On Loewy lengths of blocks
Published online by Cambridge University Press: 20 February 2014
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
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 156 , Issue 3 , May 2014 , pp. 555 - 570
- Copyright
- Copyright © Cambridge Philosophical Society 2014
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