On inner automorphisms and certain central automorphisms of groups

Azhdari, Zahedeh; Akhavan-Malayeri, Mehri

doi:10.1007/s13226-014-0069-4

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Cited by 3 publications

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“…In [2,4] we characterized all finitely generated groups for which C * = Inn G . In [3,5], we find certain necessary and sufficient conditions on G such that Aut M N G be equal to Z Inn G ,…”

Section: Introductionmentioning

confidence: 99%

Central Automorphisms and Inner Automorphisms in Finitely Generated Groups

Azhdari

2016

Communications in Algebra

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Section: Introductionmentioning

confidence: 99%

Central Automorphisms and Inner Automorphisms in Finitely Generated Groups

Azhdari

2016

Communications in Algebra

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Equality of derival automorphisms and certain automorphisms in finitely generated groups

Azhdari

2019

J. Algebra Appl.

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Let [Formula: see text] be a group and [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] 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: see text], respectively. We know that in a finite [Formula: see text]-group [Formula: see text] of class 2, [Formula: see text] if and only if [Formula: see text] is cyclic and [Formula: see text], where [Formula: see text] is the group of all derival automorphisms of [Formula: see text] which fix [Formula: see text] elementwise. In this paper, we characterize all finite nilpotent groups of class 2 for which [Formula: see text] or [Formula: see text] is equal to [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]. Also, we characterize all finitely generated nilpotent groups of class 2 for which [Formula: see text] is equal to [Formula: see text] and give some interesting corollaries in this regard.

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On equality of certain subcentral automorphisms in finite p-groups

Azhdari

2023

J. Algebra Appl.

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Let [Formula: see text] be a group and [Formula: see text] be the group of all automorphisms of [Formula: see text]. In this paper, we study the structure of certain subgroups of the automorphisms group [Formula: see text] and give necessary and sufficient conditions for equality between certain subcentral automorphisms. As consequence of these results, we state a number of interesting corollaries about central automorphisms, autocentral automorphisms and derival automorphisms for finite [Formula: see text]-groups.

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On inner automorphisms and certain central automorphisms of groups

Cited by 3 publications

References 9 publications

Central Automorphisms and Inner Automorphisms in Finitely Generated Groups

Central Automorphisms and Inner Automorphisms in Finitely Generated Groups

Equality of derival automorphisms and certain automorphisms in finitely generated groups

On equality of certain subcentral automorphisms in finite p-groups

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