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

Tiep, Pham Huu; Zalesskii, Alexander E.

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

Authors

Description

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 $p^{a-1}(p-1)$.
57 pages. Proc. London Math. Soc., to appear