﻿ 4次对称群S4的广义交换度 The Generalized Commutativity Degree of 4-Latters Symmetric Group S4

Pure Mathematics
Vol.07 No.03(2017), Article ID:20532,5 pages
10.12677/PM.2017.73021

The Generalized Commutativity Degree of 4-Latters Symmetric Group S4

Xin Li, Fang Zhou

Department of Mathematics, Taiyuan Normal University, Jinzhong Shanxi

Received: Apr. 29th, 2017; accepted: May 13th, 2017; published: May 17th, 2017

ABSTRACT

The generalized commutativity degree and subgroup commutativity degree of 4-letters symmetric group S4 are obtained by using modified elements and normalization of symmetric group Sn.

Keywords:Modified Element, Normalization, Commutativity Degree, Symmetric Group

4次对称群S4的广义交换度

1. 引言

2个平凡子群：

9个2阶子群：

4个3阶子群：

7个4阶子群：

4个6阶子群：

3个8阶子群：

1个12阶群

2. 子群的正规化子

2.1. 2阶子群

2.2. 3阶子群

2.3. 4阶子群

2.4. 6阶子群

2.5. 8阶子群

2.6. 12阶子群

3. Sn的广义交换度

4. 结束语

The Generalized Commutativity Degree of 4-Latters Symmetric Group S4[J]. 理论数学, 2017, 07(03): 163-167. http://dx.doi.org/10.12677/PM.2017.73021

1. 1. Tărnăuceanu, M. (2009) Subgroup Commutativity Degrees of Finite Groups. Journal of Algebra, 321, 2508-2520. https://doi.org/10.1016/j.jalgebra.2009.02.010

2. 2. Russo, F. (2009) The Generalized Commutativity Degree in a Finite Group. Acta Universitatis Apulensis. Mathematics-Informatics, 18, 161-167.

3. 3. 周峰, 周芳, 刘合国. 有限群的广义交换度[J]. 数学年刊, 2016, 37A(2): 1-10.

4. 4. 孙自行, 崔方达. 4次对称群 的子群个数及其证明[J]. 阜阳师范学院学报自科版, 2005, 22(4): 13-16.

5. 5. 郭旭初. 关于对称群的 中各子群的正规化子[J]. 常德师范学院学报自科版, 1999, 11(4): 4-6.