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Information Journal Paper

Title

SOME ASPECTS OF MARGINAL AUTOMORPHISMS OF A FINITE p-GROUP

Pages

  133-143

Abstract

 Let F be a free group, V be a Variety of groups defined by the set of laws V ⊆,F and G be a finite V-nilpotent p-group. The automorphism α,of G is said to be a Marginal automorphism (with respect to V ), if for all x ∈,G, x −, 1xα,∈,V ⋆, (G), where V ⋆, (G) denotes the Marginal subgroup of G. An automorphism α,of G is called an IA-automorphism if x −, 1xα,∈,G ′,for each x ∈,G. An automorphism α,of G is called a class preserving if for all x ∈,G, there exists an element gx ∈,G such that xα,= g −, 1 x xgx. Let AutV ⋆,(G), AutG ′,(G) and Autc(G) respectively, denote the group of all Marginal automorphisms, IA-automorphisms and class preserving automorphisms of G. In this paper, first we give a necessary and sufficient condition on a finite V-nilpotent p-group G such that each Marginal automorphism of G fixes the center of G element-wise. Then we characterize all finite V-nilpotent p-groups G such that AutV ⋆,(G) = AutG ′,(G). Finally, we obtain a necessary and sufficient condition for a finite V-nilpotent p-group G such that AutV ⋆,(G) = Autc(G).

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  • Cite

    APA: Copy

    Soleimani, Rasoul. (2022). SOME ASPECTS OF MARGINAL AUTOMORPHISMS OF A FINITE p-GROUP. ALGEBRAIC STRUCTURES AND THEIR APPLICATIONS, 9(1), 133-143. SID. https://sid.ir/paper/1059303/en

    Vancouver: Copy

    Soleimani Rasoul. SOME ASPECTS OF MARGINAL AUTOMORPHISMS OF A FINITE p-GROUP. ALGEBRAIC STRUCTURES AND THEIR APPLICATIONS[Internet]. 2022;9(1):133-143. Available from: https://sid.ir/paper/1059303/en

    IEEE: Copy

    Rasoul Soleimani, “SOME ASPECTS OF MARGINAL AUTOMORPHISMS OF A FINITE p-GROUP,” ALGEBRAIC STRUCTURES AND THEIR APPLICATIONS, vol. 9, no. 1, pp. 133–143, 2022, [Online]. Available: https://sid.ir/paper/1059303/en

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