### Abstract

Minimum polynomials of semisimple elements of prime power order p ^{a} of finite classical groups in (nontrivial) irreducible cross-characteristic representations are studied. In particular, an analogue of the Hall-Higman theorem is established, which shows that the degree of such a polynomial is at least p^{a-1}(p-1), with a few explicit exceptions.

Original language | English (US) |
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Pages (from-to) | 623-668 |

Number of pages | 46 |

Journal | Proceedings of the London Mathematical Society |

Volume | 97 |

Issue number | 3 |

DOIs | |

State | Published - Nov 2008 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Tiep, P. H., & Zalesskiǐ, A. E. (2008). Hall-Higman-type theorems for semisimple elements of finite classical groups.

*Proceedings of the London Mathematical Society*,*97*(3), 623-668. https://doi.org/10.1112/plms/pdn017