数学研究与评论
數學研究與評論
수학연구여평론
JOURNAL OF MATHEMATICAL RESEARCH AND EXPOSITION
2008年
3期
609-612
,共4页
PN-group%meta-nilpotent group%structure theorem
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.
