p-子群的局部性质与有限群的 p-幂零性

doi:10.12066/j.issn.1007-2861.2031

上海大学学报(自然科学版) ›› 2019, Vol. 25 ›› Issue (6): 908-917.doi: 10.12066/j.issn.1007-2861.2031

p-子群的局部性质与有限群的 p-幂零性

韩玲玲, 郭秀云()

上海大学理学院, 上海 200444

收稿日期:2017-09-25 出版日期:2019-12-30 发布日期:2019-12-31
通讯作者: 郭秀云 E-mail:xyguo@staff.shu.edu.cn
基金资助:
国家自然科学基金资助项目(11771271)

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

Lingling HAN, Xiuyun GUO()

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

摘要/Abstract

摘要：

设 $G$ 是有限群, $P$ 是 $G$ 的 Sylow $p$-子群. 通过群 $G$ 的特殊的 $p$-子群 $\it\Omega(P\cap O^{p}(G))$ 在 $G$\\中的某种交换性给出了 $G$ 为 $p$-幂零群的充分条件.

关键词: $p$-幂零群, $p$-子群, 交换群

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

中图分类号:

O152.1

韩玲玲, 郭秀云. p-子群的局部性质与有限群的 p-幂零性[J]. 上海大学学报(自然科学版), 2019, 25(6): 908-917.

Lingling HAN, Xiuyun GUO. Local properties of ${p}$-subgroups and ${p}$-nilpotency of finite groups[J]. Journal of Shanghai University（Natural Science Edition）, 2019, 25(6): 908-917.

参考文献 10

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p-子群的局部性质与有限群的 p-幂零性

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

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