Formations and Products of F(G)-Subnormal Subgroups of Finite Solvable Groups

Васильев, А. Ф.; Murashka, Viachaslau I.

doi:10.1134/s0001434620030050

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Some Applications Of F-functorials1

Introduction1

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2020

2023

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Cited by 8 publications

(2 citation statements)

References 13 publications

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“…Recall [22] that a subgroup H of G is called R-subnormal if H is subnormal in H, R . In [14,15,16,22] the products of R-subnormal subgroups were studied for R ∈ {F(G), F * (G)}. It was shown that if G is the product of two nilpotent (resp.…”

Section: Some Applications Of F-functorialsmentioning

confidence: 99%

Fitting like subgroups of finite groups

Murashka¹,

Васильев²

2021

Preprint

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In this paper the concept of F-functorial of a finite group was introduced. These functorials have many properties of the Fitting subgroup of a soluble group and the generalized Fitting subgroup of a finite group. It was shown that the set of all F-functorials is a complete distributive lattice and the cardinality of this lattice is continuum. The sharp bounds on the generalized Fitting height of mutually permutable product of two subgroups were obtained.

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Section: Some Applications Of F-functorialsmentioning

confidence: 99%

Fitting like subgroups of finite groups

Murashka¹,

Васильев²

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…If F = N, then we just obtain the notion of R-subnormal subgroup. In [11,15,18,22,23] the products of R-subnormal subgroups were studied for R ∈ {F(G), F * (G)}. It was shown that if G is the product of two nilpotent (resp.…”

Section: Introductionmentioning

confidence: 99%

On some applications of Fitting like subgroups of finite groups

Murashka¹,

Васильев²

2020

Preprint

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In this paper we study the groups all whose maximal or all Sylow subgroups are K-F-subnormal in their product the with generalizations F * (G) and F(G) of the Fitting subgroup. We prove that a hereditary formation F contains every group all whose Sylow subgroups are K-F-subnormal in their product with F * (G) if and only if F is the class of all σ-nilpotent groups for some partition σ of the set of all primes. We obtain a new characterization of the σ-nilpotent hypercenter, i.e. the F-hypercenter and the largest normal subgroup which K-F-subnormalize all Sylow subgroups coincide if and only if F is the class of all σ-nilpotent groups.

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On Finite Factorized Groups with $${\mathbb{T}}X$$-Subnormal Subgroups

Монахов

Trofimuk

2023

Ukr Math J

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Formations and Products of F(G)-Subnormal Subgroups of Finite Solvable Groups

Cited by 8 publications

References 13 publications

Fitting like subgroups of finite groups

Fitting like subgroups of finite groups

On some applications of Fitting like subgroups of finite groups

On Finite Factorized Groups with $${\mathbb{T}}X$$-Subnormal Subgroups

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