Let G be a group and H be a subgroup of G. H is called a power subgroup of G if there exists a non-negative integer m such that \(H=G^m\) , where \(G^m=\langle g^m\mid g\in G\rangle \) . In this paper, a group G is called a power simple group if G has only trivial power subgroup. The basic properties of finite power simple groups are investigated. Furthermore, we prove that G is a solvable power simple group if and only if G is a p-group with \(\exp (G)=p\) . We also determine one special case of non-solvable power simple groups without non-trivial direct product factors.
