Lawther, Ross and Liebeck, Martin W. and Seitz, Gary M. (2002) *Fixed point ratios in actions of finite exceptional groups of lie type.* Pacific Journal of Mathematics, 205 (2). pp. 393-464. ISSN 0030-8730

## Abstract

Let G be a finite exceptional group of Lie type acting transitively on a set Ø. For x in G, the fixed point ratio of x is the proportion of elements of Ø which are fixed by x. We obtain new bounds for such fixed point ratios. When a point-stabilizer is parabolic we use character theory; and in other cases, we use results on an analogous problem for algebraic groups in Lawther, Liebeck & Seitz, 2002. These give dimension bounds on fixed point spaces of elements of exceptional algebraic groups, which we apply by passing to finite groups via a Frobenius morphism.

Item Type: | Article |
---|---|

Journal or Publication Title: | Pacific Journal of Mathematics |

Subjects: | Q Science > QA Mathematics |

Departments: | Faculty of Science and Technology > Mathematics and Statistics |

ID Code: | 19279 |

Deposited By: | ep_ss_importer |

Deposited On: | 19 Nov 2008 16:58 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 07 Jan 2015 13:10 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/19279 |

### Actions (login required)

View Item |