Skip Navigation



Proceedings of the London Mathematical Society Advance Access published online on June 24, 2008
Proceedings of the London Mathematical Society, doi:10.1112/plms/pdn024
This Article
Right arrow FREE Full Text (PDF) Freely available
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Burness, T. C.
Right arrow Articles by Shalev, A.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2008 London Mathematical Society

Base sizes for simple groups and a conjecture of Cameron

Timothy C. Burness

School of Mathematics
University of Southampton
Southampton SO17 1BJ
United Kingdom
burness@soton.ac.uk

Martin W. Liebeck

Department of Mathematics
Imperial College
London
SW7 2BZ
United Kingdom

Aner Shalev

Einstein Institute of Mathematics
The Hebrew University of Jerusalem
Jerusalem 91904
Israel
shalev@math.huji.ac.il

Received 28 March 2007. Revision received 19 December 2007.

Let G be a permutation group on a finite set {Omega}. A base for G is a subset B {subseteq} {Omega} with pointwise stabilizer in G that is trivial; we write b(G) for the smallest size of a base for G. In this paper we prove that b(G) ≤ 6 if G is an almost simple group of exceptional Lie type and {Omega} is a primitive faithful G-set. An important consequence of this result, when combined with other recent work, is that b(G) ≤ 7 for any almost simple group G in a non-standard action, proving a conjecture of Cameron. The proof is probabilistic and uses bounds on fixed point ratios.

2000 Mathematics Subject Classification 20B15 (primary), 20P05 (secondary).

The first author acknowledges the support of a Junior Research Fellowship from St John's College, Oxford, and a Lady Davis Fellowship from The Hebrew University of Jerusalem.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.