# Automorphisms of a finite $p$-group with cyclic Frattini subgroup

Document Type: Research Paper

Author

Payame Noor University

Abstract

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 $|Aut^{\Phi}(G):Inn(G)|=p$‎.

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