Let H be a subgroup of G. Need to prove that Z(G) intersect H is contained in Z(H) (Z= center of the group, i.e the subset of elements in G that commute with every element of G). From this result I then need to verify that Z(G) intersect H is a normal subgroup of H. I am unsure how to do the first part of this so any help would be great, for the second part is it that Z(G) intersect H is normal in H because anything that is commutative in all of G will also be commutative in H?