Let n > 1. Let (a... as) ESn be a cycle and let o ES, be arbitrary. Show that oo (a,..., as) oo- (o(a).....o(a.)) in Sn. (Note this is an equality between maps. Hence, in order to show this equality you need to show that both sides are equal after applying them to an arbitrary element b of {1,2....,n}. To do so you will need to distinguish whether b belongs to {o(a),...,o (as)} or not.)