| 有限群的广义交换度 |
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| 引用本文： | 周 峰,周 芳,刘合国.有限群的广义交换度[J].数学年刊A辑(中文版),2016,37(2):127-136. |
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| 作者姓名： | 周 峰 周 芳 刘合国 |
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| 作者单位： | 湖北大学数学系, 武汉 430062. E-mail: thoufeng@163.com,太原师范学院数学系, 太原 030619. E-mail: fangzhou20@aliyun.con,通讯作者. 湖北大学数学系, 武汉 430062. E-mail: ghliu@hubu.edu.cn |
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| 基金项目： | 本文受到国家自然科学基金(No.11371124, No.11401424)的资助. |
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| 摘 要： | 给出了有限群广义交换度的一些性质.某种意义下,广义交换度测度了所有子群正规化子阶的平均值.通过考虑一类内交换群,探索了有限群的幂零性(可解性)与其广义交换度之间的关系.对于二面体群及含有循环极大子群的P-群,给出了其广义交换度的详细公式.
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| 关 键 词： | 交换 $p$-\!\!群 幂零 可解 |
| 收稿时间： | 2015/1/26 0:00:00 |
| 修稿时间： | 2015/9/20 0:00:00 |
The Generalized Commutativity Degree of Finite Groups |
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| ZHOU Feng,ZHOU Fang and LIU Heguo.The Generalized Commutativity Degree of Finite Groups[J].Chinese Annals of Mathematics,2016,37(2):127-136. |
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| Authors: | ZHOU Feng ZHOU Fang and LIU Heguo |
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| Institution: | Department of Mathematics, Hubei University,
Wuhan 430062, China.E-mail: thoufeng@163.com,Department of Mathematics, Taiyuan Normal University,
Taiyuan 030619, China. E-mail: fangzhou20@aliyun.com and Corresponding author. Department of Mathematics, Hubei University,
Wuhan 430062, China. E-mail: ghliu@hubu.edu.cn |
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| Abstract: | The authors give some properties of the generalized commutativity degree of finite groups.
This quantity measures the mean value of the orders of the normalizes in some sense.
Some limits are also obtained to investigate the connection between the nilpotency
(solvability) of a finite group $G$ and its generalized commutativity degree by
considering certain minimal non-abelian groups. Explicit formulas are obtained
for finite dihedral groups and finite $p$-groups possessing a cyclic maximal subgroup. |
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| Keywords: | Commutativity $p$-groups Nilpotent Solvable |
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