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 \({\mathrm{rk}}(G)\le 3+\sqrt{n+1}\). 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.

中文翻译：

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低等级的Frobenius组

令G为n个阶的有限Frobenius群。我们用基本方法证明，只要等级\（{\ mathrm {rk}}（G）\ le 3+ \ sqrt {n + 1} \），n就是一些素数p的幂。然后，G的Frobenius核与G的（唯一）Sylow p-子群一致。因此，我们的结果暗示了在特殊情况下Frobenius和Thompson的著名定理。