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On base sizes for symmetric groups

On base sizes for symmetric groups
On base sizes for symmetric groups
A base of a permutation group G on a set is a subset B of
such that the pointwise stabilizer of B in G is trivial. The base size of G, denoted by b(G), is the minimal cardinality of a base. Let G = Sn or An acting primitively on a set with point stabilizer H. In this note we prove that if H acts primitively on {1, . . . , n}, and does not contain An, then b(G) = 2 for all n 13. Combined
with a theorem of James, this completes the classification of primitive actions of alternating and symmetric groups which admit a base of size two
0024-6093
386-391
Burness, Timothy C.
a3b369f0-16f5-41e6-84d9-5a50f027bcd6
Guralnick, Robert M.
be6f9af7-ede7-4693-9643-659f79cc54a3
Saxl, Jan
0569f53a-4578-41d6-a5a3-4960650b6089
Burness, Timothy C.
a3b369f0-16f5-41e6-84d9-5a50f027bcd6
Guralnick, Robert M.
be6f9af7-ede7-4693-9643-659f79cc54a3
Saxl, Jan
0569f53a-4578-41d6-a5a3-4960650b6089

Burness, Timothy C., Guralnick, Robert M. and Saxl, Jan (2011) On base sizes for symmetric groups. Bulletin of the London Mathematical Society, 43 (2), 386-391.

Record type: Article

Abstract

A base of a permutation group G on a set is a subset B of
such that the pointwise stabilizer of B in G is trivial. The base size of G, denoted by b(G), is the minimal cardinality of a base. Let G = Sn or An acting primitively on a set with point stabilizer H. In this note we prove that if H acts primitively on {1, . . . , n}, and does not contain An, then b(G) = 2 for all n 13. Combined
with a theorem of James, this completes the classification of primitive actions of alternating and symmetric groups which admit a base of size two

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Published date: 2011

Identifiers

Local EPrints ID: 145455
URI: https://eprints.soton.ac.uk/id/eprint/145455
ISSN: 0024-6093
PURE UUID: 15b15390-f40d-401b-b295-d09e54ea270f

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Date deposited: 22 Apr 2010 09:20
Last modified: 18 Jul 2017 23:06

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