# On Marginal Automorphisms of a Group Fixing the Certain Subgroup

Authors

1 facaulty member

2 university of birjand

Abstract

Let W be a variety of groups defined by a set W of laws and G be a finite p-group in W. The automorphism α of a group G is said to bea marginal automorphism (with respect to W), if for all x G, x1α(x) W(G), where W(G) is the marginal subgroup of G. Let M,N be two normalsubgroups of G. By AutM(G), we mean the subgroup of Aut(G) consistingof all automorphisms which centralize G/M. AutN(G) is used to show thesubgroup of Aut(G) consisting of all automorphisms which centralize N. We denote AutN(G)AutM(G) by AutMN (G). In this paper, we obtain a necessary and sufficient condition that Autw(G) = AutW(G)W(G)(G).

Keywords

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