Finite groups with formational subnormal strictly 2-maximal subgroups

Konovalova, M. N.; Монахов, В. С.; Sokhor, Irina L.

doi:10.1080/00927872.2021.1986058

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Some Applications Of F-functorials1

Introduction1

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2023

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Cited by 3 publications

(2 citation statements)

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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

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“…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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Finite groups with strongly $$\textrm{c}$$-reachable second maximal subgroups

Monakhov,

Sokhor

2023

European Journal of Mathematics

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Finite groups with formational subnormal strictly 2-maximal subgroups

Cited by 3 publications

References 10 publications

Fitting like subgroups of finite groups

Fitting like subgroups of finite groups

On some applications of Fitting like subgroups of finite groups

Finite groups with strongly $$\textrm{c}$$-reachable second maximal subgroups

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