A. Skiba

activity

20112024

most citedA generalisation of Schenkman's theorem

7 citations · 22 across the 25 of their papers we have counts for

collaborators

25 papers

math.GR2024

A contribution to the theory of $σ$ -properties of a finite group

A-Ming Liu, Wenbin Guo, Vasily G. Safonov +1

We characterize some classes of finite soluble groups. In particular, we prove that: a finite group $G$ is supersoluble if and only if $G$ has a normal subgroup $D$ such that $G / D$ …

math.GR2023★ 1 cited

Finite groups in which generalized normality is a transitive relation

Inna N. Safonova, Alexander N. Skiba

In this paper, we discuss some well-known results and some open problems of the theory of $σ$ -properties of a group related to the study of generalized $T$ -groups.

math.GR2021

A $G$ -covering subgroup system of a finite group for some classes of $σ$ -soluble groups

A-Ming Liu, W. Guo, Inna N. Safonova +1

Let $F$ be a class of group and $G$ a finite group. Then a set $Σ$ of subgroups of $G$ is called a \emph{ $G$ -covering subgroup system} for the class $F$ if $G\in {\…

math.GR2020★ 7 cited

A generalisation of Schenkman's theorem

Stefanos Aivazidis, Ina N. Safonova, Alexander N. Skiba

Let $G$ be a finite group and let $F$ be a hereditary saturated formation. We denote by $Z_{F} (G)$ the product of all normal subgroups $N$ of $G$ suc…

math.GR2020

On $σ$ -arithmetic graphs of finite groups

Alexander N. Skiba

Let $G$ be a finite group and $σ$ a partition of the set of all? primes $P$ , that is, $σ = {σ_{i} ∣ i \in I}$ , where $P = ⋃_{i \in I} σ_{i}$ and $σ_i\cap σ_j= \emptys…

math.GR2019★ 1 cited

On a lattice characterization of finite soluble $P S T$ -groups

Zhang Chi, Alexander N. Skiba

Let $F$ be a class of finite groups and $G$ a finite group. Let $L_{F} (G)$ be the set of all subgroups $A$ of $G$ with $A^{G} / A_{G} \in F$ . A…

math.GR2018★ 2 cited

One application of the $σ$ -local formations of finite groups

Zhang Chi, Alexander N. Skiba

Throughout this paper, all groups are finite. Let $σ = {σ_{i} ∣ i \in I}$ be some partition of the set of all primes $P$ . If $n$ is an integer, the symbol $σ (n)$ denotes the…

math.GR2018

On one generalization of finite nilpotent groups

Zhang Chi, Alexander N. Skiba

Let $σ = {σ_{i} ∣ i \in I}$ be a partition of the set $P$ of all primes and $G$ a finite group. A chief factor $H / K$ of $G$ is said to be $σ$ -central if the semidirect product…

math.GR2017

On generalized $σ$ -soluble groups

Jianhong Huang, Bin Hu, Alexander N. Skiba

Let $σ = {σ_{i} ∣ i \in I}$ be a partition of the set of all primes $P$ and $G$ a finite group. Let $σ (G) = {σ_{i} : σ_{i} \cap π (G) \neq = \emptyset$ . A set $H$ of subgroups…

math.GR2017

A Robinson characterization of finite $P σ T$ -groups

Alexander N. Skiba

Let $σ = {σ_{i} ∣ i \in I}$ be some partition of the set of all primes $P$ and let $G$ be a finite group. Then $G$ is said to be $σ$ -full if $G$ has a Hall $σ_{i}$ -subgroup fo…

math.GR2017

Finite groups with systems of $K$ - $F$ -subnormal subgroups

Vladimir N. Semenchuk, Alexander N. Skiba

Let $F$ be a class of group. A subgroup $A$ of a finite group $G$ is said to be $K$ - $F$ -subnormal in $G$ if there is a subgroup chain $$A=A_{0} \leq A_{1} \leq \…

math.GR2017

Characterizations of some classes of finite $σ$ -soluble $P σ T$ -groups

Alexander N. Skiba

Let $σ = {σ_{i} ∣ i \in I}$ be some partition of the set of all primes $P$ and $G$ a finite group. $G$ is said to be $σ$ -soluble if every chief factor $H / K$ of $G$ is a $σ_{i}…

math.GR2017

On the lattice of the $σ$ -permutable subgroups of a finite group

Alexander N. Skiba

Let $σ = {σ_{i} ∣ i \in I}$ be some partition of the set of all primes $P$ , $G$ a finite group and $σ (G) = {σ_{i} ∣ σ_{i} \cap π (G) \neq = \emptyset}$ . A set $H$ of subgrou…

math.GR2017

On $H_{σ}$ -permutably embedded and $H_{σ}$ -subnormaly embedded subgroups of finite groups

Wenbin Guo, Chi Zhang, Alexander N. Skiba +1

Let $G$ be a finite group. Let $σ = {σ_{i} ∣ i \in I}$ be a partition of the set of all primes $P$ and $n$ an integer. We write $σ (n) = {σ_{i} ∣ σ_{i} \cap π (n) \neq = \emptyset}$ …

math.GR2016

On finite $P σ T$ -groups

Alexander N. Skiba

Let $σ = {σ_{i} ∣ i \in I}$ be some partition of the set of all primes $P$ and $G$ a finite group. $G$ is said to be \emph{ $σ$ -soluble} if every chief factor $H / K$ of $G$ is a…

math.GR2016

On $σ$ -semipermutable subgroups of finite groups

Wenbin Guo, Alexander N. Skiba

Let $σ = {σ_{i} ∣ i \in I}$ be some partition of the set of all primes $P$ , $G$ a finite group and $σ (G) = {σ_{i} ∣ σ_{i} \cap π (G) \neq = \emptyset}$ . A set $H$ of subgrou…

math.GR2016★ 7 cited

Finite groups whose $n$ -maximal subgroups are $σ$ -subnormal

Wenbin Guo, Alexander N. Skiba

Let $σ = {σ_{i} ∣ i \in I}$ be some partition of the set of all primes $P$ . A set $H$ of subgroups of $G$ is said to be a \emph{complete Hall $σ$ -set} of $G$ if every m…

math.GR2016★ 4 cited

On $Π$ -permutable subgroups of finite groups

Wenbin Guo, A. N. Skiba

Let $σ = {σ_{i} ∣ i \in I}$ be some partition of the set of all primes $P$ and $Π$ a non-empty subset of the set $σ$ . A set $H$ of subgroups of a finite group $G$ is sa…

math.GR2014

On one generalization of finite $U$ -critical groups

Vladimir N. Semenchuk, Alexander N. Skiba

A proper subgroup $H$ of a group $G$ is said to be: $P$ -subnormal in $G$ if there exists a chain of subgroups $H = H_{0} < H_{1} < ... < H_{n} = G$ such that $∣ H_{i} : H_{i - 1} ∣$ is a pr…

math.GR2014

Finite groups with generalized Ore supplement conditions for primary subgroups

Wenbin Guo, Alexander N. Skiba

We consider some applications of the theory of generalized Ore supplement conditions in the study of finite groups.

math.GR2013

Some new characterizations of $P S T$ -groups

Xiaolan Yi, Alexander N. Skiba

Let $H$ and $B$ be subgroups of a finite group $G$ such that $G = N_{G} (H) B$ . Then we say that $H$ is \emph{quasipermutable} (respectively \emph{ $S$ -quasipermutable}) in $G$ provided…

math.GR2013

On $n$ -maximal subgroups of finite groups

Vika A. Kovaleva, Alexander N. Skiba

We describe finite soluble groups in which every $n$ -maximal subgroup is $F$ -subnormal.

math.GR2012

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

Wenbin Guo, Alexander N. Skiba

Let $F$ be a class of groups. A chief factor $H / K$ of a group $G$ is called \emph{ $F$ -central in $G$ } provided $(H / K) ⋊ (G / C_{G} (H / K)) \in F$ . We write $Z_{…

math.GR2012

On Hall subgroups of a finite group

Wenbin Guo, Alexander N. Skiba

In the paper new criteria of existence and conjugacy of Hall subgroups of finite groups are given.

A contribution to the theory of σ-properties of a finite group

Finite groups in which generalized normality is a transitive relation

A G-covering subgroup system of a finite group for some classes of σ-soluble groups

A generalisation of Schenkman's theorem

On σ-arithmetic graphs of finite groups

On a lattice characterization of finite soluble PST-groups

One application of the σ-local formations of finite groups

On one generalization of finite nilpotent groups

On generalized σ-soluble groups

A Robinson characterization of finite PσT-groups

Finite groups with systems of K-F-subnormal subgroups

Characterizations of some classes of finite σ-soluble PσT-groups

On the lattice of the σ-permutable subgroups of a finite group

On Hσ​-permutably embedded and Hσ​-subnormaly embedded subgroups of finite groups

On finite PσT-groups

On σ-semipermutable subgroups of finite groups

Finite groups whose n-maximal subgroups are σ-subnormal

On Π-permutable subgroups of finite groups

On one generalization of finite U-critical groups

Finite groups with generalized Ore supplement conditions for primary subgroups

Some new characterizations of PST-groups

On n-maximal subgroups of finite groups

On the intersection of the F-maximal subgroups and the generalized F-hypercentre of a finite group

On Hall subgroups of a finite group

A contribution to the theory of $σ$ -properties of a finite group

A $G$ -covering subgroup system of a finite group for some classes of $σ$ -soluble groups

On $σ$ -arithmetic graphs of finite groups

On a lattice characterization of finite soluble $P S T$ -groups

One application of the $σ$ -local formations of finite groups

On generalized $σ$ -soluble groups

A Robinson characterization of finite $P σ T$ -groups

Finite groups with systems of $K$ - $F$ -subnormal subgroups

Characterizations of some classes of finite $σ$ -soluble $P σ T$ -groups

On the lattice of the $σ$ -permutable subgroups of a finite group

On $H_{σ}$ -permutably embedded and $H_{σ}$ -subnormaly embedded subgroups of finite groups

On finite $P σ T$ -groups

On $σ$ -semipermutable subgroups of finite groups

Finite groups whose $n$ -maximal subgroups are $σ$ -subnormal

On $Π$ -permutable subgroups of finite groups

On one generalization of finite $U$ -critical groups

Some new characterizations of $P S T$ -groups

On $n$ -maximal subgroups of finite groups

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