2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/170757We 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 appearRepresentation TheoryGroup Theory20C15, 20C20, 20C33, 20G05, 20G40text