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

Pham Huu Tiep; A. E. Zalesskiǐ

doi:10.1112/plms/pdn017

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

Pham Huu Tiep
, A. E. Zalesskiǐ

Mathematics

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

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	https://doi.org/10.1112/plms/pdn017
State	Published - Nov 2008

ASJC Scopus subject areas

General Mathematics

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title = "Hall-Higman-type theorems for semisimple elements of finite classical groups",

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

author = "Tiep, \{Pham Huu\} and Zalesskiǐ, \{A. E.\}",

note = "Funding Information: The first author gratefully acknowledges the support of the NSF (grant DMS-0600967), the NSA (grant H98230-04-0066), and the EPSRC (grant GR/S56511/01). The second author acknowledges the partial support from Levehulme trust (grant EM/2006/0030).",

year = "2008",

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doi = "10.1112/plms/pdn017",

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

AU - Tiep, Pham Huu

AU - Zalesskiǐ, A. E.

N1 - Funding Information: The first author gratefully acknowledges the support of the NSF (grant DMS-0600967), the NSA (grant H98230-04-0066), and the EPSRC (grant GR/S56511/01). The second author acknowledges the partial support from Levehulme trust (grant EM/2006/0030).

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.

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UR - https://www.scopus.com/pages/publications/54249089792#tab=citedBy

U2 - 10.1112/plms/pdn017

DO - 10.1112/plms/pdn017

M3 - Article

AN - SCOPUS:54249089792

SN - 0024-6115

VL - 97

SP - 623

EP - 668

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

IS - 3

ER -

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

Abstract

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