Product of Conjugacy Classes of the Alternating Group An
For a nonempty subset X of a group G and a positive integer m , the product of X , denoted by Xm ,is the set Xm = That is , Xm is the subset of G formed by considering all possible ordered products of m elements form X. In the symmetric g...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Baghdad, College of Science for Women
2012-09-01
|
| Series: | مجلة بغداد للعلوم |
| Subjects: | |
| Online Access: | http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/1398 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | For a nonempty subset X of a group G and a positive integer m , the product of X , denoted by Xm ,is the set
Xm =
That is , Xm is the subset of G formed by considering all possible ordered products of m elements form X. In the symmetric group Sn, the class Cn (n odd positive integer) split into two conjugacy classes in An denoted Cn+ and Cn- . C+ and C- were used for these two parts of Cn. This work we prove that for some odd n ,the class C of 5- cycle in Sn has the property that = An n 7 and C+ has the property that each element of C+ is conjugate to its inverse, the square of each element of it is the element of C-, these results were used to prove that C+ C- = An exceptional of I (I the identity conjugacy class), when n=5+4k , k>=0. |
|---|---|
| ISSN: | 2078-8665 2411-7986 |