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Base sizes for sporadic simple groups

Base sizes for sporadic simple groups
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 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.
0021-2172
307-333
Burness, Timothy C.
a3b369f0-16f5-41e6-84d9-5a50f027bcd6
O'Brien, E.A.
1313218d-c02d-4ca4-b415-b9022b654d18
Wilson, Robert A.
4b75cf5a-6348-4091-8a85-ac1a77c07f08
Burness, Timothy C.
a3b369f0-16f5-41e6-84d9-5a50f027bcd6
O'Brien, E.A.
1313218d-c02d-4ca4-b415-b9022b654d18
Wilson, Robert A.
4b75cf5a-6348-4091-8a85-ac1a77c07f08

Burness, Timothy C., O'Brien, E.A. and Wilson, Robert A. (2010) Base sizes for sporadic simple groups. Israel Journal of Mathematics, 177 (1), 307-333. (doi:10.1007/s11856-010-0048-3).

Record type: Article

Abstract

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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Published date: 2010

Identifiers

Local EPrints ID: 48270
URI: http://eprints.soton.ac.uk/id/eprint/48270
ISSN: 0021-2172
PURE UUID: 02ec500c-06bb-4057-8682-8dccf1c4b117

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Date deposited: 07 Sep 2007
Last modified: 16 Dec 2019 19:18

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