University of Isfahan International Journal of Group Theory 2251-7650 7 4 2018 12 01 Automorphisms of a finite $p$-group with cyclic Frattini subgroup 9 16 21219 10.22108/ijgt.2017.21219 EN Rasoul Soleimani Payame Noor University Journal Article 2016 08 08 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 https://ijgt.ui.ac.ir/article_21219_ae7d67b716884474ebab05e35cda245c.pdf