Zahedeh Azhdari

Alzahra University · Department of Mathematics

Let G be a group and let Autc(G) be the group of all central automorphisms of G. Let C∗ = CAutc(G)(Z(G)) be the set of all central automorphisms of G fixing Z(G) elementwise. In this paper, we prove that if G is a finitely generated nilpotent group of class 2, then C∗ � Inn(G) if and only if Z(G) is cyclic or Z(G) � Cm × Zr where G Z(G) has exponen...

Let G be a group and let M and N be two normal subgroups of G. Let AutMN 16 (G) 17 be the set of all automorphisms of G which centralize G/M and N. In this paper, we find certain necessary and sufficient conditions on G such that AutMN 18 (G) be equal to Z(Inn(G)), Inn(G), C∗ 19 or Autc(G). We also characterize the subgroups of a finite p-group G f...

Let G be a group and Autc(G) the group of all central automorphism of G. Let C∗ = CAutc(G)(Z(G)) be the set of all central automorphisms of G fixing Z(G) elementwise. In this paper we consider finitely generated torsion-free nilpotent groups of class 2 with cyclic center, in which Inn(G) = C∗(= Autc(G)) and we give a characterization of such groups...

Let (Formula presented.) be a group and (Formula presented.), (Formula presented.), (Formula presented.) and (Formula presented.) denote the group of all inner automorphisms, the group of all pointwise inner automorphisms, the group of all central automorphisms and the group of all derival automorphisms of (Formula presented.), respectively. We kno...

Let G be a group and Autc(G) be the group of all central automorphisms of G. We know that in a finite p-group G, Autc(G) = Inn(G) if and only if Z(G) = G′ and Z(G) is cyclic. But we shown that we cannot extend this result for infinite groups. In fact, there exist finitely generated nilpotent groups of class 2 in which G′ =Z(G) is infinite cyclic an...

Let G be a group, let M and N be two normal subgroups of G. We denote by Aut N M (G), the set of all automorphisms of G which centralize G/M and N. In this paper we investigate the structure of a group G in which one of the Inn(G) = Aut N M (G), Aut N M(G) ≤ Inn(G) or Inn(G) ≤ Aut N M(G) holds. We also discuss the problem: “what conditions on G is...

Let G be a group. An automorphism θ of a group G is pointwise inner if θ(x) is conjugate to x for any x ∈ G. We denote by Aut c (G) and C* the group of all central automorphisms and the group of all central automorphisms of G fixing Z(G) elementwise, respectively. In this paper, we introduce a natural generalization of the concept of pointwise inne...

Let G be a group and let M and N be two normal subgroups of G. Let be the set of all automorphisms of G which centralize G/M and N. In this paper, we find certain necessary and sufficient conditions on G such that be equal to Z(Inn(G)), Inn(G), C* or Autc(G). We also characterize the subgroups of a finite p-group G for which the equality holds.

Let G be a group and Aut c (G) the group of all central automorphisms of G. Let C * =C Aut c (G) (Z(G)) be the set of all central automorphisms of G fixing Z(G) element-wise. In this paper, we consider finitely generated torsion-free nilpotent groups of class 2 with cyclic center, in which Inn (G)=C * (=Aut c (G)) and we give a characterization of...