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## Homework Statement

The question is:

Let A be a subset of S

_{n}that contains all permutations alpha such that alpha can be written as a product of an even number of transpositions. Prove that A is a group with product of permutations.

I understand what I need to do to prove it, but I am not sure how to start it. Do I use:

Let alpha=(a1a2a3...an) and

beta=(b1b2b3...bn) and try to find closure,

alphabeta=(a1a2a3...an)(b1b2b3...bn)=(a1a2)(a1a3)...(a1an-1)(a1an)(b1b2)(b1b3)...(b1bn-1)(b1bn),

or am I going about it the wrong way?