Let there be some group S acting on a set Y and lets denote this action by *. : S KY

Is defined, for s S, by (s) = s, where s(y) = s y for all y Y.

(a) Prove that is faithful if, and only if, is injective.

(b) Prove that if is surjective then is transitive.

(c) Prove that can be transitive without being surjective.