Let n > 1. Let (a... as) ESn be a cycle and let o ES, be...

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Let n > 1. Let (a₁... as) ESn be a cycle and let o ES, be arbitrary. Show that oo (a₁,..., as) oo-¹ (o(a₁).....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(a₁),...,o (as)} or not.) Let n > 1. Let (a₁... as) ESn be a cycle and let o ES, be arbitrary. Show that oo (a₁,..., as) oo-¹ (o(a₁).....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(a₁),...,o (as)} or not.)

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