关于有限群的Pronormal极小子群

摘要

利用有限群G的pronormal极小子群和Sylow子群正规化子中的素数阶弱左Engel元素得到了G成为p-幂零群、幂零群和超可解群的一些充分条件,这些结果推广了已知结论.%By using pronormal minimal subgroups and weak left Engel elements of prime order of the normalizers of Sylow subgroups of a finite group G, we obtain some sufficient conditions for G to be p-nilpotent, nilpotent and supersolvable respectively,which generalize some known results.