Prove that the order of An (the subgroup of all even permutation of Sn) is (1/2)n!
And even permutation is one that must be written with an even number of transpositions (2-cycles)
The Attempt at a Solution
I know that being (1/2)n! means half of Sn is even. I think I'm supposed to show why the subgroup must be half. I have in my notes something about a mapping, it was one of those days where I couldn't read my prof's handwriting (same as always) and I wasn't feeling up to asking him what the heck the board said. Something about a mapping Phi, that maps evens into odds.
This is just one in a long line of theorems I'm studying this weekend, and my brain is about fried. Please be clear, and try not to make it too hard.