Alternating Groups

1. Apr 5, 2009

Gear300

Alternating groups apply to all even permutations in Sn for n > 2. Since n = 2 is inclusive, what got me wondering is that for such a case there are only 2 elements in S (say w and x); wouldn't that mean that the only transposition permutation would be (w x), which is an odd permutation?

2. Apr 5, 2009

jeffreydk

If you go by the fact that the order of any alternating group is $n!/2$ then you would have that the order of $A_2$ is $2!/2=1$ and therefore it's just the trivial group consisting of the identity element. Anything in the form of (wx) would be an odd permutation and therefore not in $A_2$

3. Apr 5, 2009

Gear300

I see...so it would simply imply the identity element...Thanks

4. Apr 5, 2009

No problem