The problem asks, "What is the maximum order of any element in$ A_10 $?"
$ A_10 $ is a an Alternating Group of degree n. $ A_n $ is the group of only even permutations of n symbols.
We have 10 numbers: 1 2 3 4 5 6 7 8 9 10
Size Order
10 10
8 8
6 12 6 6 6 6
4 12 20 (from 4, 5, 1 cycles) 4 (from 4 2 4 cycles) 4 (from 4 3 3) 12
