Product of Conjugacy Classes of the Alternating Group An

• Main Author: Baghdad Science Journal
• Format: Article
• Language: Arabic
• Published: College of Science for Women, University of Baghdad 2012-09-01
• Series: Baghdad Science Journal
• Subjects: " conjugacy classes ,split, Alternating Group, Product"
• Online Access: http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/1398
• ISSN: 2078-8665; 2411-7986

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.