On commuting automorphisms of groups

Deaconescu, Marian; Silberberg, Gheorghe; Walls, Gary L.

doi:10.1007/bf02638378

Cited by 27 publications

(6 citation statements)

References 9 publications

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“…Furthermore, we proved that for any prime and for all integers there exists a non-, p-group of order . [3]. Further, the authors in [4] have proved that the inner automorphisms which belong to are precisely the inner automorphisms which are induced by 2-Engel elements.…”

Section: An Automorphism Of Is Called a Commuting Automorphism If Formentioning

confidence: 99%

“…We denote the set of all commuting automorphisms of by It seems tha t for the first time, the commuting automorphisms are defined, in various rings(see [1], [5] and [10]). Deaconsecu, Silberberg and Walls in [3] showed that even though h as a number of group properties, it does not necessarily form a subgroup of . A group is called -group if the set forms a subgroup of .…”

Section: An Automorphism Of Is Called a Commuting Automorphism If Formentioning

confidence: 99%

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Some Remarks on Commuting Fixed Point Free Automorphisms of Groups

Akhavan-Malayeri¹

2016

Mathematical Researches

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In this article we will find necessary and sufficient conditions for a fixed point free automorphism (fpf automorphism) of a group to be a commuting automorphism. For a given prime we find the smallest order of a non abelian p-group admitting a commuting fixed point free automorphism. We prove that a group of order p 3 having a commuting fpf automorphism, has a restricted structure. Moreover, we prove that if a finite group admits a fpf automorphism of order 4, then the converse of Laffey's result holds in G 1 .

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Section: An Automorphism Of Is Called a Commuting Automorphism If Formentioning

confidence: 99%

Section: An Automorphism Of Is Called a Commuting Automorphism If Formentioning

confidence: 99%

Some Remarks on Commuting Fixed Point Free Automorphisms of Groups

Akhavan-Malayeri¹

2016

Mathematical Researches

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“…In 2002, Deaconescu, Silberberg and Walls proved that the set A(G) is not always a subgroup of Aut(G) but it has many of the properties of a group (see [5]). Definition 1.1.…”

Section: Introductionmentioning

confidence: 99%

Commuting automorphisms of finite 2-groups of almost maximal class, I

2019

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Let [Formula: see text] be a group. If the set [Formula: see text] for all [Formula: see text] forms a subgroup of [Formula: see text], then [Formula: see text] is called [Formula: see text]-group. Let [Formula: see text] be an odd prime. Recently it has been proven that a finite [Formula: see text]-group of almost maximal class is an [Formula: see text]-group. For finite 2-groups of almost maximal class, the situation is much more complicated. This paper deals with the case [Formula: see text]. We prove that a 2-group of almost maximal class is an [Formula: see text]-group. We show the minimum coclass of a non-[Formula: see text], [Formula: see text]-group is equal to 3. We also discuss the direct product of certain [Formula: see text]-groups and subsequently we give some applications of our results.

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“…This kind of automorphisms were first studied for various classes of rings [1,9,11]. M. Desconesco and G. Silberbers [7] proved that A(G) do not necessarily form a subgroup of Aut(G). We also recall that a central automorphism of a group…”

Section: Introductionmentioning

confidence: 99%

On tensor analogues of commuting automorphisms and central automorphisms

Mohammadzadeh,

Golmakani,

Hokmabadi

et al. 2019

Preprint

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On commuting automorphisms of groups

Cited by 27 publications

References 9 publications

Some Remarks on Commuting Fixed Point Free Automorphisms of Groups

Some Remarks on Commuting Fixed Point Free Automorphisms of Groups

Commuting automorphisms of finite 2-groups of almost maximal class, I

On tensor analogues of commuting automorphisms and central automorphisms

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