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Information Journal Paper

Title

The Automorphism Group of Non-Abelian Group of Order p^4

Author(s)

 Orfi Reza | Issue Writer Certificate 

Pages

  197-204

Abstract

 Determining the order and the structure of the Automorphism group of a finite p-group is an important problem in group theory. There have been a number of studies of the Automorphism group of-p groups. Most of them deal with the order of Aut (G) the Automorphism group of G, . Moreover various attempts have been made to find a structure for the Automorphism group of a finite p-group. Following [2], [29], two groups are isoclinic if their commutator subgroups and central quotients are isomorphic and their commutator operations are essentially the same. We use the classification of p-groups by James [5], which based on isoclinism. By using [5] we have ten non-isoclinic families of non-abelian groups of order p^4. Let G be a finite non-abelian group of order p^4, Aut p (G)be the Sylow p--subgroup of Aut (G) and  = (G) be the Frattini subgroup of G. It is well-known [7, Satz III. 3. 17] that the Aut^  (G) the group of all automorphisms of Gcentralizing G/ (G)', is normal p-subgroup of Aut (G). In this paper we give a structure theorem for Aut p (G). Also we prove that if G is p-group of maximal class then Aut p (G)=Aut  (G) or Aut p (G) is a split extension of Aut  (G) by a cyclic group of order p.

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    APA: Copy

    Orfi, Reza. (2020). The Automorphism Group of Non-Abelian Group of Order p^4. MATHEMATICAL RESEARCHES, 5(2 ), 197-204. SID. https://sid.ir/paper/377460/en

    Vancouver: Copy

    Orfi Reza. The Automorphism Group of Non-Abelian Group of Order p^4. MATHEMATICAL RESEARCHES[Internet]. 2020;5(2 ):197-204. Available from: https://sid.ir/paper/377460/en

    IEEE: Copy

    Reza Orfi, “The Automorphism Group of Non-Abelian Group of Order p^4,” MATHEMATICAL RESEARCHES, vol. 5, no. 2 , pp. 197–204, 2020, [Online]. Available: https://sid.ir/paper/377460/en

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