Let G be a group. The center Z(G) of G is the subset {g E GIVh E G: gh = hg} of G. (i) Show that Z(G) is a normal subgroup of G. (ii) Let G be non-abelian and |G|=p3 for some prime p. Show that IZ(G)] = p. Determine the center of the dihedral group D4- (iii)

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