Base sizes for sporadic simple groups
Let G be a permutation group acting on a set . A subset of is a base for G if its pointwise stabilizer in G is trivial. We write b(G) for the minimal size of a base for G. We determine the precise value of b(G) for every primitive almost simple sporadic group G, with the exception of two cases in...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
2010.
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| Subjects: | |
| Online Access: | Get fulltext |
| Summary: | Let G be a permutation group acting on a set . A subset of is a base for G if its pointwise stabilizer in G is trivial. We write b(G) for the minimal size of a base for G. We determine the precise value of b(G) for every primitive almost simple sporadic group G, with the exception of two cases involving the Baby Monster group. As a corollary, we deduce that b(G) 6 7, with equality if and only if G is the Mathieu group M24 in its natural action on 24 points. This settles a conjecture of Cameron. |
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