Reduced fusion systems over 2-groups of small order
| Autor: | Joana Ventura, Kasper K. S. Andersen, Bob Oliver |
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| Rok vydání: | 2016 |
| Předmět: |
Pure mathematics
Fusion Algebra and Number Theory 010102 general mathematics Sylow theorems 010103 numerical & computational mathematics Group Theory (math.GR) 01 natural sciences Range (mathematics) Fusion system Simple group FOS: Mathematics Order (group theory) Classification of finite simple groups 0101 mathematics Mathematics - Group Theory 20D20 Mathematics |
| DOI: | 10.48550/arxiv.1606.05059 |
| Popis: | We prove, when $S$ is a $2$-group of order at most $2^9$, that each reduced fusion system over $S$ is the fusion system of a finite simple group and is tame. It then follows that each saturated fusion system over a $2$-group of order at most $2^9$ is realizable. What is most interesting about this result is the method of proof: we show that among $2$-groups with order in this range, the ones which can be Sylow $2$-subgroups of finite simple groups are almost completely determined by criteria based on Bender's classification of groups with strongly $2$-embedded subgroups. |
| Databáze: | OpenAIRE |
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