Rasoul Soleimani - Payame Noor University

Let $G$ be a group and $Aut^{\Phi}(G)$ denote the group of all automorphisms of $G$ centralizing $G/\Phi(G)$ elementwise‎. ‎In this paper‎, ‎we characterize the finite $p$-groups $G$ with cyclic Frattini subgroup for which $|Aut^{\Phi}(G):Inn(G)|=p$‎.

‎‎Automorphism group‎, ‎Finite $p$-group‎, ‎Frattini subgroup‎