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arXiv · 0810.0855

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

Pham Huu Tiep·Alexander E. Zalesskii
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Abstract

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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Pham Huu Tiep, Alexander E. Zalesskii. 2008-10-05. Hall-Higman type theorems for semisimple elements of finite classical groups. https://arxiv.org/abs/0810.0855

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