If p is an odd prime, prove the following.

a) If G is a group of order $\displaystyle (p-1)p^2$, then G has a unique Sylow p-subgroup.

b) There are at least four groups of order $\displaystyle (p-1)p^2 $which are pairwise nonisomorphic.

I know little about Sylow's subgroups.

$\displaystyle |G|=(p-1)p^2 $

$\displaystyle n_i\equiv 1 \ (\text{mod} \ i) $