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

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 Added by Pham H. Tiep
 Publication date 2008
  fields
and research's language is English




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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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