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
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
2011
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), .
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
Text
baselms2.pdf
- Accepted Manuscript
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Published date: 2011
Identifiers
Local EPrints ID: 145455
URI: http://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: 14 Mar 2024 00:50
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Contributors
Author:
Timothy C. Burness
Author:
Robert M. Guralnick
Author:
Jan Saxl
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