Journal of Shanghai University(Natural Science Edition) ›› 2019, Vol. 25 ›› Issue (6): 908-917.doi: 10.12066/j.issn.1007-2861.2031

• Research Articles • Previous Articles     Next Articles

Local properties of ${p}$-subgroups and ${p}$-nilpotency of finite groups

Lingling HAN, Xiuyun GUO()   

  1. College of Sciences, Shanghai University, Shanghai, 200444, China
  • Received:2017-09-25 Online:2019-12-30 Published:2019-12-31
  • Contact: Xiuyun GUO E-mail:xyguo@staff.shu.edu.cn

Abstract:

Let $G$ be a finite group and $P$ be a Sylow $p$-subgroup of $G$. Several sufficient conditions for a finite group G to be $p$-nilpotent group are given by means of some kind of commutativity of a special $p$-subgroup $\it\Omega(P\cap O^{p}(G))$ in $G$.

Key words: $p$-nilpotent group, $p$-subgroup, abelian group

CLC Number: