| 王玉雷,刘合国,吴佐慧.Frattini子群循环的有限$p$-群中的非交换集和极大Abel子群[J].数学年刊A辑,2016,37(4):451~462 |
| Frattini子群循环的有限$p$-群中的非交换集和极大Abel子群 |
| On Non-commuting Sets and Maximal Abelian Subgroups in a Finite $p$-Group with a\Cyclic Frattini Subgroup |
| Received:January 21, 2014 Revised:July 12, 2014 |
| DOI： |
| 中文关键词: 有限$p$-\!\!群, Frattini子群, 非交换集, 极大Abel子群 |
| 英文关键词:Finite $p$-groups, Frattini subgroups, Non-commuting sets, Maximal abelian subgroups |
| 基金项目:本文受到国家自然科学基金 (No.11301150, No.11371124),
河南省自然科学基金(No.142300410134)和河南工业大学创新人才计划项目(No.11CXRC19)的资助. |
|
| Hits: 6265 |
| Download times: 874 |
| 中文摘要: |
| 设$G$是一个群, $X$是$G$的一个子集, 若对于任意$x,y\in X$且$x\neq y$, 都有$xy\neq yx$, 则称$X$是$G$的一个非交换集.
进一步, 如果对于$G$中的任意其它非交换子集$Y$, 都有$|X|\geq|Y|$, 那么称$X$是$G$的一个极大非交换集.
文中确定了Frattini子群循环的有限$p$-\!\!群中极大非交换集和极大Abel子群的势. |
| 英文摘要: |
| Let $G$ be a group. A subset $X$ in $G$ is said to be
non-commuting if $xy\neq yx$ for any $x,y\in X$ with $x\neq y$. Further, if $|X|\geq|Y|$ for any other non-commuting subset
$Y$ in $G$, then $X$ is said to
be a maximal non-commuting set.
In this paper, the cardinalities of a maximal
non-commuting set and a maximal abelian subgroup in a finite $p$-group with a cyclic Frattini subgroup are determined. |
| View Full Text View/Add Comment Download reader |
| Close |
|
|
|
|
|
