“具有幂零局部子群的有限群”一文的注记

称有限群$G$为一个PN-群若 $G$非幂零群,且对$G$的每一个$p$-子群$P$, 或者$P$是$G$的正规子群, 或者$P \subseteq Z_\infty(G)$， 或者$N_G(P)$是幂零群, $\forall p \in \pi(G)$. 本文证明了PN-群是亚幂零群. 特别地, PN-群是可解的 且给出了PN-群结构定理的一个初等的、直观的、简洁的证明.

Notes on ``Finite Groups with Nilpotent Local Subgroups'

A finite group G is called PN-group if G is not nilpotent and for every p-subgroup P of G, there holds that either P is normal in G or P C Z∞(G) or NG(P) is nilpotent, p ∈π(G).In this paper, we prove that PN-group is meta-nilpotent, especially, PN-group is solvable. In addition, we give an elementary, intuitionistie, compact proof of the structure theorem of PN-group.