Central Automorphism Groups for Semidirect Product of p-Groups

Abstract

Let ℤp²⋊ϕℤp be the semi-direct product of ℤp² and ℤp with respect to ϕ,(ϕ is homomorphism from ℤp to automorphismsgroup of ℤp²). In this work, the group AutC(ℤ3²⋊ϕℤ₃) of all central automorphismsof ℤ3²⋊ϕℤ₃ is studied and we determinethe form of central automorphisms of ℤ3²⋊ϕℤ3 .