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

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

2008-10-05

arxiv.org/abs/0810.0855v1

Mathematics

Representation Theory

57 pages. Proc. London Math. Soc., to appear

Scientific paper

We prove an analogue of the celebrated Hall-Higman theorem, which gives a
lower bound for the degree of the minimal polynomial of any semisimple element
of prime power order $p^{a}$ of a finite classical group in any nontrivial
irreducible cross characteristic representation. With a few explicit
exceptions, this degree is at least $p^{a-1}(p-1)$.

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