Central Automorphism Groups for Semidirect Product of p-Groups

Abstract

Let ℤ_p²⋊_ϕℤ_p be the semi-direct product of ℤ_p² and ℤ_p with respect to ϕ, (ϕ is homomorphism from ℤ_p to automorphisms group of ℤ_p²). In this work, the group Aut_C(ℤ_3²⋊_ϕℤ₃) of all central automorphisms of ℤ_3²⋊_ϕℤ₃ is studied and we determine the form of central automorphisms of ℤ_3²⋊_ϕℤ₃ . 

Keywords

• P-group,Semi-direct product

References

1. J. E. AdneyT.Yen, Automorphisms of p-groups, Illinois J. Math. 9(1965), 137-143. A. R. Jamali and H. Mousavi, On the central automorphism group of finite p-groups, Algebra Coolog. 9(1) (2002), 7-14. G. Saeden Stahl, J. Laine, G. Behm, On p-groups of low power order, Master Thesis, KTH, (2010).