Frobenius groups of low rank

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