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Hall–Higman‐type theorems for semisimple elements of finite classical groups
Author(s) -
Tiep Pham Huu,
Zalesskiĭ A. E.
Publication year - 2008
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdn017
Subject(s) - mathematics , type (biology) , pure mathematics , biology , ecology
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.