### 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) |
---|---|

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 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Proceedings of the London Mathematical Society*,

*97*(3), 623-668. https://doi.org/10.1112/plms/pdn017

**Hall-Higman-type theorems for semisimple elements of finite classical groups.** / Tiep, Pham Huu; Zalesskiǐ, A. E.

Research output: Contribution to journal › Article

*Proceedings of the London Mathematical Society*, vol. 97, no. 3, pp. 623-668. https://doi.org/10.1112/plms/pdn017

}

TY - JOUR

T1 - Hall-Higman-type theorems for semisimple elements of finite classical groups

AU - Tiep, Pham Huu

AU - Zalesskiǐ, A. E.

PY - 2008/11

Y1 - 2008/11

N2 - 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 pa-1(p-1), with a few explicit exceptions.

AB - 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 pa-1(p-1), with a few explicit exceptions.

UR - http://www.scopus.com/inward/record.url?scp=54249089792&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=54249089792&partnerID=8YFLogxK

U2 - 10.1112/plms/pdn017

DO - 10.1112/plms/pdn017

M3 - Article

AN - SCOPUS:54249089792

VL - 97

SP - 623

EP - 668

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

SN - 0024-6115

IS - 3

ER -