A little problem with permutations.

[gipc]

Let A_n be a subgroup of S_n that includes all the even permutations. How many permutations of order 6 does A_6 include?

 

[Petr Mugver]

What do you mean by "order of a permutation"?

 

[adriank]

The order of the permutation as an element of a group, of course.

Remember that if you decompose an element x of S_n as a product of disjoint cycles, then the order of x is equal to the lcm of the lengths of the cycles. You will find that if you decompose an element x of S₆ of order 6 into disjoint cycles, then x must be odd.