Blocks with transitive fusion systems
Abstract
Suppose that all nontrivial subsections of a $p$-block $B$ are conjugate (where $p$ is a prime). By using the classification of the finite simple groups, we prove that the defect groups of $B$ are either extraspecial of order $p^3$ with $p \in \{3,5\}$ or elementary abelian.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2014
- DOI:
- 10.48550/arXiv.1410.5705
- arXiv:
- arXiv:1410.5705
- Bibcode:
- 2014arXiv1410.5705H
- Keywords:
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- Mathematics - Representation Theory;
- Mathematics - Algebraic Topology;
- Mathematics - Group Theory;
- 20Cxx