关于Thompson定理的一个注记

A Note on Thompson Theorem

证明有限群G是幂零的,如果满足:G′幂零,G有素数r阶自同构α使得rπ(CG(α)),并且G有α-不变的幂零极大子群H使得CG(α)≤Φ(H)且H的Sylow2-子群的幂零类≤2.该结果推广了Thompson定理.

It is proved that a finite group G is nilpotent if G′ is nilpotent and G has prime r order automorphism a such that r∈r（CG（a）） for a-invarant nilpotent maximal subgroup H of G with CG（a） ≤Ф（H） and c（H2）≤2. This conclusion generalizing the theorem of Thompson.