Covering Theorem for the Alternating Group An

The product oftwo subsets C,K of a group G is deflned asCK={xyl X ⊆〕,y ⊆e power of Cm is deflned inductively bycl=c,c2=cc,cm=CCm~1=Cm‐ lC. The smallest integer in such that G ⊂ Cm is called exponent of C or some times referred as Cm covers G. In this paper the cottugaCy class C ofthe symmetric gЮ up Sn(n Odd) oftype 3-cycle is studied,and the following results are obtained: 1-CC covers A5 C iS the cottugacy class oftype 313 2-CCC covers A7 C iSthe cottugacy class oftype 314 3-Ccovers An C iSthe cottugacy Class oftype 31n3 n Odd 4-CC includcs the cottugaCy Class oftype 221n4 here we callit K