Frobenius groups of low rank

摘要

Let G be a finite Frobenius group of degree n. We show, by elementary means, that n is a power of some prime p provided the rank rk(G) <= 3 + root n+1. Then the Frobenius kernel of G agrees with the (unique) Sylow p-subgroup of G. So our result implies the celebrated theorems of Frobenius and Thompson in a special situation.