Perfect groups and normal subgroups related to an automorphism

Ganjali, Masoumeh; Erfanian, Ahmad

doi:10.1007/s11587-016-0307-7

Cited by 3 publications

(4 citation statements)

References 4 publications

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“…. The relative perfectness of abelian groups was studied by authors of [4]. In this paper, we may continue our investigation on relative perfect groups and prove some new results on some classes of finite non-abelian -groups.…”

Section: ) (G D mentioning

confidence: 78%

“…Furthermore, they proved some results on relative normal and absolute normal subgroups of some classes of finite groups. In [4], they introduced an α-perfect group G, a group which is equal to its α-commutator subgroup, for a fixed automorphism α of G. If ′ is the ordinary commutator subgroup of G, then…”

Section: ) (G D mentioning

confidence: 99%

“…In this section, we recall the definition of an α-perfect group for a fixed automorphism α. At first, we present some results on relative perfect groups that were proved in [4]. Finally, we may add some new results on non-abelian relative perfect groups.…”

Section: Relative Perfect Groupsmentioning

confidence: 99%

“…It might be important to find all proper absolute normal subgroups of given finite group . In [3] and [4], the structure of absolute normal subgroups of some classes of finite groups were given. For instance, we have the following results.…”

Section: Relative Perfect Groupsmentioning

confidence: 99%

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Some Notes on Relative Commutators

Ganjali

Erfanian

2020

InPrime:Ind.Jour.Pure.Applied.Math

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Let G be a group and α ϵ Aut(G). An α-commutator of elements x, y ϵ G is defined as [x, y]α = x-1y-1xyα. In 2015, Barzegar et al. introduced an α-commutator of elements of G and defined a new generalization of nilpotent groups by using the definition of α-commutators which is called an α-nilpotent group. They also introduced an α-commutator subgroup of G, denoted by Dα(G) which is a subgroup generated by all α-commutators. In 2016, an α-perfect group, a group that is equal to its α-commutator subgroup, was introduced by authors of this paper and the properties of such group was investigated. They proved some results on α-perfect abelian groups and showed that a cyclic group G of even order is not α-perfect for any α ϵ Aut(G). In this paper, we may continue our investigation on α-perfect groups and in addition to studying the relative perfectness of some classes of finite p-groups, we provide an example of a non-abelian α-perfect 2-group.

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Section: ) (G D mentioning

confidence: 78%

Section: ) (G D mentioning

confidence: 99%

Section: Relative Perfect Groupsmentioning

confidence: 99%

Section: Relative Perfect Groupsmentioning

confidence: 99%

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Some Notes on Relative Commutators

Ganjali

Erfanian

2020

InPrime:Ind.Jour.Pure.Applied.Math

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Nilpotent groups related to an automorphism

Erfanian

Ganjali

2018

Proc Math Sci

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Relation between the left and right cosets of an α-normal subgroup

Mahatma

Hadi

Sudarwanto

2021

J. Phys.: Conf. Ser.

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Let G be a group and α be an automorphism of G. In 2016, Ganjali and Erfanian introduced the notion of a normal subgroup related to α, called the α-normal subgroup. It is basically known that if N is an ordinary normal subgroup of G then every right coset Ng is actually the left coset gN. This fact allows us to define the product of two right cosets naturally, thus inducing the quotient group. This research investigates the relation between the left and right cosets of the relative normal subgroup. As we have done in the classic version, we then define the product of two right cosets in a natural way and continue with the construction of a, say, relative quotient group.

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Perfect groups and normal subgroups related to an automorphism

Cited by 3 publications

References 4 publications

Some Notes on Relative Commutators

Some Notes on Relative Commutators

Nilpotent groups related to an automorphism

Relation between the left and right cosets of an α-normal subgroup

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