Product of Conjugacy Classes of the Alternating Group An | ||
| Baghdad Science Journal | ||
| Article 1, Volume 9, Issue 3, September 2012, Pages 565-568 | ||
| Author | ||
| Lamia Hassan Raheef | ||
| Abstract | ||
| 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. | ||
| Keywords | ||
| Key Words; split; Alternating Group; Product | ||
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