  The power graph $P(G)$ of a finite group $G$ is the undirected simple graph
with vertex set $G$, where two elements are adjacent if one is a power of the
other. In this paper, the matching numbers of power graphs of finite groups are
investigated. We give upper and lower bounds, and conditions for the power
graph of a group to possess a perfect matching. We give a formula for the
matching number for any finite nilpotent group. In addition, using some
elementary number theory, we show that the matching number of the enhanced
power graph $P_e(G)$ of $G$ (in which two elements are adjacent if both are
powers of a common element) is equal to that of the power graph of $G$.
