On Commuting Automorphisms of<i>p</i>-Groups

Vosooghpour, Fatemeh; Akhavan-Malayeri, Mehri

doi:10.1080/00927872.2011.617022

Cited by 11 publications

(4 citation statements)

References 9 publications

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“…A group is called -group if the set forms a subgroup of . In [13] we proved that the minimum order of a non-p-group is . We also found the s mallest group order of a non p-group.…”

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

confidence: 95%

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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“…A group is called -group if the set forms a subgroup of . In [13] we proved that the minimum order of a non-p-group is . We also found the s mallest group order of a non p-group.…”

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

confidence: 95%

Some Remarks on Commuting Fixed Point Free Automorphisms of Groups

Akhavan-Malayeri¹

2016

Mathematical Researches

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“…Vosooghpour also proved this result. But Vosooghpour's result never got published, except in her phd thesis in 2014 [14].…”

Section: Introductionmentioning

confidence: 99%

“…Vosooghpour and Akhavan-Malayeri in [12] proved that for a given prime p, minimum order of a non-A p-group is p 5 . They proved that there exists a non-A p-group of order p n for all n ≥ 5.…”

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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“…In [7] we proved that the minimum order of a non-A(G) p-group is p 5 . We also found the smallest group order of a non-A(G) p-group.…”

Section: Introductionmentioning

confidence: 99%

COMMUTING AUTOMORPHISM OF p-GROUPS WITH CYCLIC MAXIMAL SUBGROUPS

Vosooghpour¹,

Kargarian²,

Akhavan-Malayeri³

2013

Communications of the Korean Mathematical Society

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Abstract. Let G be a group and let p be a prime number. If the set A(G) of all commuting automorphisms of G forms a subgroup of Aut(G), then G is called A(G)-group. In this paper we show that any p-group with cyclic maximal subgroup is an A(G)-group. We also find the structure of the group A(G) and we show that A(G) = Autc(G). Moreover, we prove that for any prime p and all integers n ≥ 3, there exists a nonabelian A(G)-group of order p n in which A(G) = Autc(G). If p > 2, then A(G) ∼ = Zp × Z p n−2 and if p = 2, then A(G) ∼ = Z 2 × Z 2 × Z 2 n−3 or Z 2 × Z 2 .

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On Commuting Automorphisms ofp-Groups

Cited by 11 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

COMMUTING AUTOMORPHISM OF p-GROUPS WITH CYCLIC MAXIMAL SUBGROUPS

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