Notes on ＂Finite Groups with Nilpotent Local Subgroups＂  

作　　者：LI Yang Ming 

机构地区：[1]Department of Mathematics, Guangdong College of Education, Guangdong 510310, China

出　　处：《Journal of Mathematical Research and Exposition》2008年第3期609-612,共4页数学研究与评论（英文版）

基　　金：the National Natural Science Foundation of China （No. 10571181）; the Natural Science Foundation of Guangdong Province （No. 06023728）.Acknowledgement The author wishes to thank Prof. Guo Wenbin for his help. The author also thanks the referees for their helpful comments.

摘　　要：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 lohtain in Z∞（G） or NG（P） is nilpotent, arbitary 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, intuitionistic, compact proof of the structure theorem of PN- group.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 lohtain in Z∞（G） or NG（P） is nilpotent, arbitary 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, intuitionistic, compact proof of the structure theorem of PN- group.

关 键 词：PN-group meta-nilpotent group structure theorem. 

分 类 号：O152.1[理学—数学]