For each of the groups G and subsets H, show that H is a normal subgroup of G and give an isomorphism G\HG where G is some well-chosen, familiar group.

1. G=ZZ,H={{n,n}nZ}.
2. G=U(7)=(Z/7Z),H={squaresinG}.
3. G=U(55),H={squaresinG}. [Hint: U(55)U(5)U(11)Z/10ZZ/4Z. What do squares correspond to under this isomorphism?]