I found an old past paper solution that says the following:
If
Then .
Why? And why is the number of elements in of order 5 equal to ??
hey I was having some trouble here and I was wondering if anybody could assist me.
Show that (1 2 3 4 5) is conjugate to (1 3 5 2 4) in but not in .
Clearly (4 5 3 2) will work and this is odd, so not in A5. but why can't we find an even permutation that will work for the conjugation?
Well, my first inclination (and this may be incorrect) was to use the fact that the product of any number of even permutations is even (and the odd analogue) to show that . You could do this by showing that is even and is odd. The problem would follow.