(a) Show that if G is an abelian group and H ≤ G is a
non-trivial subgroup, then the action G on G/H on the set of
left cosets of H in G is never faithful
(b)Suppose that G has order 75, and let H ≤ G be a subgroup of
index 3. Show that, if H' ≤ G is any subgroup of index 3, then
in fact H' = H