Thread: Permutation group order

Show that contains an element of order 15.

Note: is the group of even permutation of 8.

I really don't know how to start this proof, please help.

Originally Posted by tttcomrader

Show that contains an element of order 15.

Note: is the group of even permutation of 8.

I really don't know how to start this proof, please help.

Let be a cycle with length . And let be a cycle with length . Then the order of the permutation is equal to . So the idea is to find an even cycle of length 5 and another even cycle with length 3 and take their product.

Originally Posted by Bernhard Riemann

Let be a cycle with length . And let be a cycle with length . Then the order of the permutation is equal to . So the idea is to find an even cycle of length 5 and another even cycle with length 3 and take their product.

Okay how about I give you my example and you confirm the details.

1)Consider this is an even permutation, why? So .

2)Consider this is an even permutation, why? So .

3)Define this is an even permutation, why? So .

4)By my previous comment .

So I pick O = (1 2 3) and r = (4 5 6 7 8 9), they are both even permutations, and O has length 3, r has length 5, so ord(Or) = 15.

Thank you!