V. I. Murashka

activity

20122026

most citedOn partially conjugate-permutable subgroups of finite groups

3 citations · 5 across the 24 of their papers we have counts for

collaborators

24 papers

math.GR2026

On the intersection of $F$ -maximal subgroups of a finite group

Viachaslau I. Murashka, Yana A. Kuptsova

We investigate the properties of the intersection $Int_{F} (G)$ of all $F$ -maximal subgroups of a finite group $G$ for a hereditary formation $\mathfr…

math.GR2025

On the Length of a Maximal Subgroup of a Finite Group

Viachaslau I. Murashka, Alexander F. Vasil'ev

For a finite group $G$ and its maximal subgroup $M$ we proved that the generalized Fitting height of $M$ can't be less by 2 than the generalized Fitting height of $G$ and the non-$…

math.GR2024

Formations of Finite Groups in Polynomial Time: the $F$ -Hypercenter

Viachaslau I. Murashka

For a wide family of formations $F$ (which includes Baer-local formations) it is proved that the $F$ -hypercenter of a permutation finite group can be compute…

math.GR2024

Formations of Finite Groups in Polynomial Time: the $F$ -Radical

Viachaslau I. Murashka

For a Baer-local (composition) Fitting formation $F$ the polynomial time algorithm for the computation of the $F$ -radical of a permutation group is suggested.…

math.GR2024

Constructing regular saturated formations of finite soluble groups

Viachaslau I. Murashka

For a formation $F$ of finite groups consider a graph whose vertices are elements of a finite group and two vertices are connected by an edge if and only if they generat…

math.GR2024

$σ$ -properties of finite groups in polynomial time

Viachaslau I. Murashka

Let $H, K$ be subgroups of the permutation group $G$ of degree $n$ with $K ⊴ G$ and $σ$ be a partition of the set of all different prime divisors of $∣ G / K ∣$ . We prove…

math.GR2024

A test for a local formation of finite groups to be a formation of soluble groups with the Shemetkov property

V. I. Murashka

L.A. Shemetkov posed a Problem 9.74 in Kourovka Notebook to find all local formations $F$ of finite groups such that every finite minimal non- $F$ -group is eit…

math.GR2023

Arithmetic graphs and the products of finite groups

Viachaslau I. Murashka

The Hawkes graph $Γ_{H} (G)$ of $G$ is the directed graph whose vertex set coincides with $π (G)$ and it has the edge $(p, q)$ whenever $q \in π (G / O_{p^{'}, p} (G))$ . The Sylow graph $Γ_{s} (G)$ …

math.GR2023

On the Generalized Fitting Height and Nonsoluble Length of the Mutually Permutable Products of Finite Groups

Viachaslau I. Murashka, Alexander F. Vasil'ev

The generalized Fitting height $h^{*} (G)$ of a finite group $G$ is the least number $h$ such that $F_{h}^{*} (G) = G$ , where $F_{(0)}^{*} (G) = 1$ , and $\mathrm{F}_{(i+1)…

math.GR2022

Formations of Finite Groups in Polynomial Time: $F$ -residuals and $F$ -subnormality

Viachaslau I. Murashka

For a wide family of formations $F$ it is proved that the $F$ -residual of a permutation finite group can be computed in a polynomial time. Moreover, if in th…

math.GR2021

On ECP-Groups

Viachaslau I. Murashka

According to T. Foguel a subgroup $H$ of a group $G$ is called conjugate-permutable if $H H^{x} = H^{x} H$ for every $x \in G$ . Mingyao Xu and Qinhai Zhang studied finite groups with every…

math.GR2021

Fitting like subgroups of finite groups

Viachaslau I. Murashka, Alexander F. Vasil'ev

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 gen…

math.GR2021

A generalization of Hall's theorem on hypercenter

Viachaslau I. Murashka, Alexander F. Vasil'ev

Let $σ$ be a partition of the set of all primes and $F$ be a hereditary formation. We described all formations $F$ for which the $F$ -hypercenter a…

math.GR2020

On a generalization of one Kramer's theorem

Viachaslau I. Murashka

Yangming Li and Xianhua Li in 2012 proposed a conjecture that generalizes O.U. Kramer's result about supersoluble groups. Here we proved that this conjecture is false in the genera…

math.GR2020

On some applications of Fitting like subgroups of finite groups

Viachaslau I. Murashka, Alexander F. Vasil'ev

In this paper we study the groups all whose maximal or all Sylow subgroups are $K$ - $F$ -subnormal in their product the with generalizations of the Fitting subgroup $\math…

math.GR2019

On one question of Shemetkov about composition formations

Viachaslau I. Murashka

In this paper one construction of composition formations was introduced. This construction contains formations of quasinilpotent groups, $c$ -supersoluble groups, groups defined by…

math.GR2017

On Autonilpotent Finite Groups

V. I. Murashka

In the paper autonilpotent groups were characterized as groups $G$ such that $Aut G$ stabilizes some chain of subgroups of $G$ . It was shown that a $p$ -group is autonilpote…

math.GR2017

On classes of finite groups with simple non-abelian chief factors

V. I. Murashka

Let $J$ be a class of non-abelian simple groups and $X$ be a class of groups. A chief factor $H / K$ of a group $G$ is called $X$ -central in $G$ prov…

math.GR2016

On the quasi- $F$ -hypercenter of a finite group

V. I. Murashka

In this paper some properties of the $F^{*}$ -hypercenter of a finite group are studied where $F^{*}$ is the class of all finite quasi- $F$ -groups for a…

math.GR2016

On a generalization of the concept of S-permutable subgroup of a finite group

V. I. Murashka

Let $σ = {π_{i} ∣ i \in I$ and $π_{i} \cap π_{j} = \emptyset$ for all $i \neq = j}$ be a partition of the set of all primes into mutually disjoint subsets. In this paper we considered subgroups…

math.GR2015

On generalizations of Baer's theorems about the hypercenter of a finite group

V. I. Murashka

We investigate the intersection of normalizers and $F$ -subnormalizers of different types of systems of subgroups ( $F$ -maximal, Sylow, cyclic primary). We desc…

math.GR2015

Arithmetic graphs of finite groups

V. I. Murashka, A. F. Vasil'ev

In this paper we introduced an arithmetic graph function which associates with every group G the directed graph whose vertices corresponds to the divisors of |G|. With the help of…

math.GR2013★ 2 cited

One formation of finite groups

Viachaslau I. Murashka

It is shown that two formations of finite groups, one was introduced by V.S. Monakhov and V.N. Kniahina and another one was introduced by R. Brandl, are coincides.

math.GR2012★ 3 cited

On partially conjugate-permutable subgroups of finite groups

V. I. Murashka, A. F. Vasil'ev

Let $R$ be a subset of a group $G$ . We call a subgroup $H$ of $G$ the $R$ -conjugate-permutable subgroup of $G$ , if $H H^{x} = H^{x} H$ for all $x \in R$ . This concept is a generalizatio…

On the intersection of F-maximal subgroups of a finite group

On the Length of a Maximal Subgroup of a Finite Group

Formations of Finite Groups in Polynomial Time: the F-Hypercenter

Formations of Finite Groups in Polynomial Time: the F-Radical

Constructing regular saturated formations of finite soluble groups

σ-properties of finite groups in polynomial time

A test for a local formation of finite groups to be a formation of soluble groups with the Shemetkov property

Arithmetic graphs and the products of finite groups

On the Generalized Fitting Height and Nonsoluble Length of the Mutually Permutable Products of Finite Groups

Formations of Finite Groups in Polynomial Time: F-residuals and F-subnormality

On ECP-Groups

Fitting like subgroups of finite groups

A generalization of Hall's theorem on hypercenter

On a generalization of one Kramer's theorem

On some applications of Fitting like subgroups of finite groups

On one question of Shemetkov about composition formations

On Autonilpotent Finite Groups

On classes of finite groups with simple non-abelian chief factors

On the quasi-F-hypercenter of a finite group

On a generalization of the concept of S-permutable subgroup of a finite group

On generalizations of Baer's theorems about the hypercenter of a finite group

Arithmetic graphs of finite groups

One formation of finite groups

On partially conjugate-permutable subgroups of finite groups

On the intersection of $F$ -maximal subgroups of a finite group

Formations of Finite Groups in Polynomial Time: the $F$ -Hypercenter

Formations of Finite Groups in Polynomial Time: the $F$ -Radical

$σ$ -properties of finite groups in polynomial time

Formations of Finite Groups in Polynomial Time: $F$ -residuals and $F$ -subnormality

On the quasi- $F$ -hypercenter of a finite group