On base sizes for actions of finite classical groups
Let G be a finite almost simple classical group and let ? be a faithful primitive non-standard G-set. A base for G is a subset B C_ ? whose pointwise stabilizer is trivial; we write b(G) for the minimal size of a base for G. A well-known conjecture of Cameron and Kantor asserts that there exists an...
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| Format: | Article |
| Language: | English |
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2007-06.
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| Online Access: | Get fulltext Get fulltext |
| LEADER | 01007 am a22001333u 4500 | ||
|---|---|---|---|
| 001 | 46634 | ||
| 042 | |a dc | ||
| 100 | 1 | 0 | |a Burness, Timothy C. |e author |
| 245 | 0 | 0 | |a On base sizes for actions of finite classical groups |
| 260 | |c 2007-06. | ||
| 856 | |z Get fulltext |u https://eprints.soton.ac.uk/46634/1/tcb7.pdf | ||
| 856 | |z Get fulltext |u https://eprints.soton.ac.uk/46634/2/Burness_07.pdf | ||
| 520 | |a Let G be a finite almost simple classical group and let ? be a faithful primitive non-standard G-set. A base for G is a subset B C_ ? whose pointwise stabilizer is trivial; we write b(G) for the minimal size of a base for G. A well-known conjecture of Cameron and Kantor asserts that there exists an absolute constant c such that b(G) ? c for all such groups G, and the existence of such an undetermined constant has been established by Liebeck and Shalev. In this paper we prove that either b(G) ? 4, or G = U6(2).2, G? = U4(3).22 and b(G) = 5. The proof is probabilistic, using bounds on fixed point ratios. | ||
| 655 | 7 | |a Article | |