Guest kelkul Posted December 7, 2004 Share Posted December 7, 2004 Suppose n is an integer and n>=2. Show that An is a normal subgroup of Sn and compute Sn/An. That is, find a known group to which Sn/An is isomorphic. Link to comment Share on other sites More sharing options...
matt grime Posted December 7, 2004 Share Posted December 7, 2004 What are the orders of An and Sn? Hence what is the order of Sn/An? How many groups are there of that order? Link to comment Share on other sites More sharing options...
Guest kelkul Posted December 8, 2004 Share Posted December 8, 2004 This is all that is given in the question. I don't know what the orders are or anything else. I need help though..haha Link to comment Share on other sites More sharing options...
matt grime Posted December 8, 2004 Share Posted December 8, 2004 S_n is the permutation group on n objects. It has n! elements. A_n is the subgroup of even elements. If you don't know what that is then you need to learn it, from your notes and understand why it has n!/2 elements. You also should immediately see that there are two cosets of A_n in S_n and thus that A_n is normal so the quotient group exists and has order.....? Link to comment Share on other sites More sharing options...
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