  The power graph of a group $G$ is the graph whose vertex set is $G$ and two
distinct vertices are adjacent if one is a power of the other. This paper
investigates the minimal separating sets of power graphs of finite groups. For
power graphs of finite cyclic groups, certain minimal separating sets are
obtained. Consequently, a sharp upper bound for their connectivity is supplied.
Further, the components of proper power graphs of $p$-groups are studied. In
particular, the number of components of that of abelian $p$-groups are
determined.
