Alexander Nikolaevich Skiba

Francisk Skorina Gomel State University

*This is an algorithmically generated author record based on publicly available information.

See Latest Publications

See Most Cited Publications

SciProfiles

ORCID Profile

Google Scholar

Current Organizations / Institutes

The organizations/institutes from the scholar's latest article

Research Subjects

Research Interests

Alexander Nikolaevich Skiba has a total of 92 co-authors. Here are the top co-authors by number of shared publications:

Wenbin Guo
School of Mathematics and Statistics, Hainan University, Haikou, China
38 shared publications
Inna Nikolaevna Safonova
Belarusian State University
21 shared publications
A.-Ming Liu
School of Science, Hainan University, Haikou, China
18 shared publications
Wenbin Guo
Department of Mathematics, School of Science, Hainan University, Haikou, Hainan, PR China
16 shared publications
Jianhong Huang
School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, China
14 shared publications
Vasily Grigorevich Safonov
Institute of Mathematics of the National Academy of Sciences of Belarus, Minsk, Belarus
14 shared publications

Latest Publications

Sort by

Open Access
Website
Google Scholar
- 18 January 2026
- Published by MDPI AG in Mathematics
On Two Classes of Sublattices of the Subgroup Lattice of a Finite Group
by Muzhi Wang, A-Ming Liu, Alexander N. Skiba
Let G denote a finite group; $σ = {σ_{i} ∣ i \in I \subseteq {0} \cup N}$ be some partition of the set of all primes $P$ , where $0 \in I$ ; $I$ be a class of finite $σ_{0}$ -groups that is closed under extensions, epimorphic images, and subgroups and contains all finite soluble $σ_{0}$ -groups. We say that a subgroup A of G is $σ_{I}$ -subnormal in G if there is a subgroup chain $A = A_{0} \leq A_{1} \leq \dots \leq A_{t} = G$ such that either $A_{i - 1} ⊴ A_{i}$ , $A_{i} / {(A_{i - 1})}_{A_{i}} \in I$ , or $A_{i} / {(A_{i - 1})}_{A_{i}}$ is a $σ_{j}$ -group for some $j \neq 0$ . In this paper, we prove that the set $L_{σ_{I}} (G)$ of all $σ_{I}$ -subnormal subgroups of G and some proper subsets of $L_{σ_{I}} (G)$ form sublattices of the lattice of all subgroups of G.
Website
Google Scholar
- 18 January 2026
- Published by MDPI AG in Mathematics
Open Access
On Two Classes of Sublattices of the Subgroup Lattice of a Finite Group
by Muzhi Wang, A-Ming Liu, Alexander N. Skiba
Let G denote a finite group; $σ = {σ_{i} ∣ i \in I \subseteq {0} \cup N}$ be some partition of the set of all primes $P$ , where $0 \in I$ ; $I$ be a class of finite $σ_{0}$ -groups that is closed under extensions, epimorphic images, and subgroups and contains all finite soluble $σ_{0}$ -groups. We say that a subgroup A of G is $σ_{I}$ -subnormal in G if there is a subgroup chain $A = A_{0} \leq A_{1} \leq \dots \leq A_{t} = G$ such that either $A_{i - 1} ⊴ A_{i}$ , $A_{i} / {(A_{i - 1})}_{A_{i}} \in I$ , or $A_{i} / {(A_{i - 1})}_{A_{i}}$ is a $σ_{j}$ -group for some $j \neq 0$ . In this paper, we prove that the set $L_{σ_{I}} (G)$ of all $σ_{I}$ -subnormal subgroups of G and some proper subsets of $L_{σ_{I}} (G)$ form sublattices of the lattice of all subgroups of G.
Website
Google Scholar
- 24 February 2025
- Published by European Mathematical Society - EMS - Publishing House GmbH in Rendiconti del Seminario Matematico della Università di Padova
On weakly $N$-subnormal subgroups of finite groups
by A-Ming Liu, Muzhi Wang, Vasily G. Safonov, Alexander N. Skiba
Let G be a finite group and A, N\leq G . Then A_{\operatorname{sn} G} is the subnormal core of A in G , that is, the subgroup of A generated by all subnormal subgroups of G , contained in A ; A^{\operatorname{sn} G} is the subnormal closure of A in G , that is, the intersection of all subnormal subgroups of G containing A . We say that a subgroup A of G is (i) N -subnormal in G if N\cap A^{\operatorname{sn} G}=N\cap A_{\operatorname{sn} G} ; (ii) weakly N -subnormal in G if for some subnormal subgroup T of G we have AT=G and A\cap T\leq S\leq A , where S is N -subnormal in G . In this paper, we consider some applications of these two concepts. In particular, we prove that a finite group G is soluble if and only if G has a normal subgroup N with soluble factor G/N such that in each maximal chain M_{3}< M_{2}< M_{1}< M_{0}= G of G of length 3 , at least one of the subgroups M_{3} , M_{2} or M_{1} is weakly N -subnormal in G .
Website
Google Scholar
- 24 February 2025
- Published by European Mathematical Society - EMS - Publishing House GmbH in Rendiconti del Seminario Matematico della Università di Padova
On weakly $N$-subnormal subgroups of finite groups
by A-Ming Liu, Muzhi Wang, Vasily G. Safonov, Alexander N. Skiba
Let G be a finite group and A, N\leq G . Then A_{\operatorname{sn} G} is the subnormal core of A in G , that is, the subgroup of A generated by all subnormal subgroups of G , contained in A ; A^{\operatorname{sn} G} is the subnormal closure of A in G , that is, the intersection of all subnormal subgroups of G containing A . We say that a subgroup A of G is (i) N -subnormal in G if N\cap A^{\operatorname{sn} G}=N\cap A_{\operatorname{sn} G} ; (ii) weakly N -subnormal in G if for some subnormal subgroup T of G we have AT=G and A\cap T\leq S\leq A , where S is N -subnormal in G . In this paper, we consider some applications of these two concepts. In particular, we prove that a finite group G is soluble if and only if G has a normal subgroup N with soluble factor G/N such that in each maximal chain M_{3}< M_{2}< M_{1}< M_{0}= G of G of length 3 , at least one of the subgroups M_{3} , M_{2} or M_{1} is weakly N -subnormal in G .
Website
Google Scholar
- 1 December 2024
- Published by Pleiades Publishing Ltd in Proceedings of the Steklov Institute of Mathematics
Lattice Characterizations of $p$-Soluble and $p$-Supersoluble Finite Groups
by A-Ming Liu, Sizhe Wang, V. G. Safonov, A. N. Skiba
Let $G$ be a finite group, and let ${\mathcal{L}}(G)$ be the lattice of all subgroups of $G$. A subgroup $M$ of $G$ is called modular in $G$ if $M$ is a modular element (in the Kurosh sense) of the lattice ${\mathcal{L}}(G)$, i.e., if (1) $\langle X,M\cap Z\rangle=\langle X,M\rangle\cap Z$ for all $X\leq G,Z\leq G$ such that $X\leq Z$, and (2) $\langle M,Y\cap Z\rangle=\langle M,Y\rangle\cap Z$ for all $Y\leq G,Z\leq G$ such that $M\leq Z$. If $A$ is a subgroup of $G$, then $A_{mG}$ is the subgroup of $A$ generated by all its subgroups that are modular in $G$. We say that a subgroup $A$ is $N$-modular in $G$ ($N\leq G$) if, for some modular subgroup $T$ of $G$ containing $A$, $N$ avoids the pair $(T,A_{mG})$, i.e., $N\cap T=N\cap A_{mG}$. Using these notions, we give new characterizations of $p$-soluble and $p$-supersoluble finite groups.
Website
Google Scholar
- 1 December 2024
- Published by Pleiades Publishing Ltd in Proceedings of the Steklov Institute of Mathematics
Lattice Characterizations of $p$-Soluble and $p$-Supersoluble Finite Groups
by A-Ming Liu, Sizhe Wang, V. G. Safonov, A. N. Skiba
Let $G$ be a finite group, and let ${\mathcal{L}}(G)$ be the lattice of all subgroups of $G$. A subgroup $M$ of $G$ is called modular in $G$ if $M$ is a modular element (in the Kurosh sense) of the lattice ${\mathcal{L}}(G)$, i.e., if (1) $\langle X,M\cap Z\rangle=\langle X,M\rangle\cap Z$ for all $X\leq G,Z\leq G$ such that $X\leq Z$, and (2) $\langle M,Y\cap Z\rangle=\langle M,Y\rangle\cap Z$ for all $Y\leq G,Z\leq G$ such that $M\leq Z$. If $A$ is a subgroup of $G$, then $A_{mG}$ is the subgroup of $A$ generated by all its subgroups that are modular in $G$. We say that a subgroup $A$ is $N$-modular in $G$ ($N\leq G$) if, for some modular subgroup $T$ of $G$ containing $A$, $N$ avoids the pair $(T,A_{mG})$, i.e., $N\cap T=N\cap A_{mG}$. Using these notions, we give new characterizations of $p$-soluble and $p$-supersoluble finite groups.
Website
Google Scholar
- 1 December 2024
- Published by Pleiades Publishing Ltd in Mathematical Notes
Finite Groups with Generalized Subnormal $\mathfrak{F}$-Critical Subgroups
by S. Wang, A. M. Liu, V. G. Safonov, A. N. Skiba
Let $G$ be a finite group and let $A$ be a subgroup of $G$. Let $A_{\operatorname{sn}G}$ be the subgroup of $A$ generated by all subnormal subgroups of $G$ contained in $A$, and let $A^{\operatorname{sn}G}$ be the intersection of all subnormal subgroups of $G$ containing $A$. Let $N\le G$. Then we say that $A$ is $N$-subnormal in $G$ if $N$ avoids every composition factor $H/K$ of $G$ between $A_{\operatorname{sn}G}$ and $A^{\operatorname{sn}G}$, i.e., $N\cap H= N\cap K$. In this paper, we give applications of $N$-subnormality to the theory of groups with given $\mathfrak{F}$-critical subgroups. In particular, using this notion, we give new characterizations of finite solvable groups, metanilpotent groups, and groups with nilpotent derived subgroup $G'$.
Website
Google Scholar
- 1 December 2024
- Published by Pleiades Publishing Ltd in Mathematical Notes
Finite Groups with Generalized Subnormal $\mathfrak{F}$-Critical Subgroups
by S. Wang, A. M. Liu, V. G. Safonov, A. N. Skiba
Let $G$ be a finite group and let $A$ be a subgroup of $G$. Let $A_{\operatorname{sn}G}$ be the subgroup of $A$ generated by all subnormal subgroups of $G$ contained in $A$, and let $A^{\operatorname{sn}G}$ be the intersection of all subnormal subgroups of $G$ containing $A$. Let $N\le G$. Then we say that $A$ is $N$-subnormal in $G$ if $N$ avoids every composition factor $H/K$ of $G$ between $A_{\operatorname{sn}G}$ and $A^{\operatorname{sn}G}$, i.e., $N\cap H= N\cap K$. In this paper, we give applications of $N$-subnormality to the theory of groups with given $\mathfrak{F}$-critical subgroups. In particular, using this notion, we give new characterizations of finite solvable groups, metanilpotent groups, and groups with nilpotent derived subgroup $G'$.
Website
Google Scholar
- 1 December 2024
- Published by Krasovskii Institute of Mathematics and Mechanics UB RAS in Trudy Instituta Matematiki i Mekhaniki UrO RAN
Решеточные характеризации $p$-разрешимых и $p$-сверхразрешимых конечных групп
by А-Мин Лю, Сичэ Ван, В. Г. Сафонов, А. Н. Скиба
УДК 512.542 MSC: 20D10, 20D30 DOI: 10.21538/0134-4889-2024-30-4-180-187 Работа выполнена при поддержке Национального фонда естественных наук Китая (No. 12101165, No. 12171126) и НФЕНК-БРФФИ (No. 12311530761). Исследования третьего и четвертого авторов выполнены при поддержке Белорусского республиканского фонда фундаментальных исследований (No. Ф24КИ-021). Пусть $G$ — конечная
Website
Google Scholar
- 1 December 2024
- Published by Krasovskii Institute of Mathematics and Mechanics UB RAS in Trudy Instituta Matematiki i Mekhaniki UrO RAN
Решеточные характеризации $p$-разрешимых и $p$-сверхразрешимых конечных групп
by А-Мин Лю, Сичэ Ван, В. Г. Сафонов, А. Н. Скиба
УДК 512.542 MSC: 20D10, 20D30 DOI: 10.21538/0134-4889-2024-30-4-180-187 Работа выполнена при поддержке Национального фонда естественных наук Китая (No. 12101165, No. 12171126) и НФЕНК-БРФФИ (No. 12311530761). Исследования третьего и четвертого авторов выполнены при поддержке Белорусского республиканского фонда фундаментальных исследований (No. Ф24КИ-021). Пусть $G$ — конечная
Website
Google Scholar
- 20 November 2024
- Published by Springer Nature in Acta Mathematica Hungarica
On an application of the lattice of $\sigma$-permutable subgroups of a finite group
by A. -M. Liu, V. G. Safonov, A. N. Skiba, S. Wang
Website
Google Scholar
- 20 November 2024
- Published by Springer Nature in Acta Mathematica Hungarica
On an application of the lattice of $\sigma$-permutable subgroups of a finite group
by A. -M. Liu, V. G. Safonov, A. N. Skiba, S. Wang
Website
Google Scholar
- 18 November 2024
- Published by Steklov Mathematical Institute
Конечные группы с обобщенно субнормальными $\mathfrak{F}$-критическими подгруппами
by Sizhe Wang, A. M. Liu, Vasily Grigorevich Safonov, Alexander Nikolaevich Skiba
Пусть $G$ - конечная группа и $A$ - некоторая ее подгруппа. Пусть $A_{\operatorname{sn}G}$ - подгруппа $A$, порожденная всеми субнормальными подгруппами группы $G$, содержащимися в $A$, и $A^{\operatorname{sn}G}$ - пересечение всех субнормальных подгруппы группы $G$, содержащих $A$. Пусть $N\leqslant G$. Тогда мы говорим, что $A$ $N$-субнормальна в $G$, если $N$ изолирует каждый композиционный фактор $H/K$ группы $G$ между $A_{\operatorname{sn}G}$ и $A^{\operatorname{sn}G}$, т.е. $N\cap H= N\cap K$. В данной работе мы даем приложения $N$-субнормальности в теории групп с заданными $\mathfrak{F}$-критическими подгруппами. В частности, используя это понятие, мы даем новые характеризации конечных разрешимых, метанильпотентных групп и групп с нильпотентной производной подгруппой $G'$. Библиография: 26 названий.
Website
Google Scholar
- 18 November 2024
- Published by Steklov Mathematical Institute
Конечные группы с обобщенно субнормальными $\mathfrak{F}$-критическими подгруппами
by Sizhe Wang, A. M. Liu, Vasily Grigorevich Safonov, Alexander Nikolaevich Skiba
Пусть $G$ - конечная группа и $A$ - некоторая ее подгруппа. Пусть $A_{\operatorname{sn}G}$ - подгруппа $A$, порожденная всеми субнормальными подгруппами группы $G$, содержащимися в $A$, и $A^{\operatorname{sn}G}$ - пересечение всех субнормальных подгруппы группы $G$, содержащих $A$. Пусть $N\leqslant G$. Тогда мы говорим, что $A$ $N$-субнормальна в $G$, если $N$ изолирует каждый композиционный фактор $H/K$ группы $G$ между $A_{\operatorname{sn}G}$ и $A^{\operatorname{sn}G}$, т.е. $N\cap H= N\cap K$. В данной работе мы даем приложения $N$-субнормальности в теории групп с заданными $\mathfrak{F}$-критическими подгруппами. В частности, используя это понятие, мы даем новые характеризации конечных разрешимых, метанильпотентных групп и групп с нильпотентной производной подгруппой $G'$. Библиография: 26 названий.
Website
Google Scholar
- 18 November 2024
- Published by Springer Nature in Ricerche di Matematica
Characterizations of some classes of finite soluble groups
by A-Ming Liu, Zhigang Wang, Vasily G. Safonov, Alexander N. Skiba
Website
Google Scholar
- 18 November 2024
- Published by Springer Nature in Ricerche di Matematica
Characterizations of some classes of finite soluble groups
by A-Ming Liu, Zhigang Wang, Vasily G. Safonov, Alexander N. Skiba
Website
Google Scholar
- 25 September 2024
- Published by World Scientific Pub Co Pte Ltd in Journal of Algebra and Its Applications
A criterion for modularity of the subgroup lattice of a finite soluble group
by A-Ming Liu, Sizhe Wang, Vasily G. Safonov, Alexander N. Skiba
Let [ ] be a finite group and [ ] the subgroup lattice of [ ]. A subgroup [ ] of [ ] is called: (i) modular in [ ], if [ ] is a modular element (in the sense of Kurosh) of the lattice [ ]; (ii) submodular in [ ] if [ ] has a chain of subgroups [ ], where [ ] is modular in [ ] for all [ ]. If [ ] is a subgroup of [ ], then we denote by [ ] the subgroup of [ ], generated by all of its subgroups that are modular in [ ]. We say that a subgroup [ ] is [ ]-modular in [ ] ([ ]), if for some modular subgroup [ ] of [ ], containing [ ], [ ] avoids the pair [ ], i.e. [ ]. We prove that if [ ] is a soluble finite group and each of its submodular subgroups is [ ]-modular in [ ], where [ ] is the nilpotent residual of [ ], then the lattice [ ] is modular.
Website
Google Scholar
- 25 September 2024
- Published by World Scientific Pub Co Pte Ltd in Journal of Algebra and Its Applications
A criterion for modularity of the subgroup lattice of a finite soluble group
by A-Ming Liu, Sizhe Wang, Vasily G. Safonov, Alexander N. Skiba
Let [ ] be a finite group and [ ] the subgroup lattice of [ ]. A subgroup [ ] of [ ] is called: (i) modular in [ ], if [ ] is a modular element (in the sense of Kurosh) of the lattice [ ]; (ii) submodular in [ ] if [ ] has a chain of subgroups [ ], where [ ] is modular in [ ] for all [ ]. If [ ] is a subgroup of [ ], then we denote by [ ] the subgroup of [ ], generated by all of its subgroups that are modular in [ ]. We say that a subgroup [ ] is [ ]-modular in [ ] ([ ]), if for some modular subgroup [ ] of [ ], containing [ ], [ ] avoids the pair [ ], i.e. [ ]. We prove that if [ ] is a soluble finite group and each of its submodular subgroups is [ ]-modular in [ ], where [ ] is the nilpotent residual of [ ], then the lattice [ ] is modular.
Website
Google Scholar
- 28 August 2024
- Published by Walter de Gruyter GmbH in Journal of Group Theory
On 𝜎-permutable subgroups of 𝜎-soluble finite groups
by Zhigang Wang, A-Ming Liu, Vasily G. Safonov, Alexander N. Skiba
Let $σ = {σ_{i} ∣ i \in I}$ be some partition of the set of all primes and 𝐺 a finite group. Then 𝐺 is said to be 𝜎-full if 𝐺 has a Hall $σ_{i}$ -subgroup for all $i \in I$ and 𝜎-primary if 𝐺 is a $σ_{i}$ -group for some 𝑖. In addition, 𝐺 is 𝜎-soluble if every chief factor of 𝐺 is 𝜎-primary and 𝜎-nilpotent if 𝐺 is a direct product of 𝜎-primary groups. We write $G^{N_{σ}}$ for the 𝜎-nilpotent residual of 𝐺, which is the intersection of all normal subgroups 𝑁 of 𝐺 with 𝜎-nilpotent $G / N$ . A subgroup 𝐴 of 𝐺 is said to be 𝜎-permutable in 𝐺 provided 𝐺 is 𝜎-full and 𝐴 permutes with all Hall $σ_{i}$ -subgroups 𝐻 of 𝐺 (that is, $A H = H A$ ) for all 𝑖. And 𝐴 is 𝜎-subnormal in 𝐺 if there is a subgroup chain $A = A_{0} \leq A_{1} \leq \dots \leq A_{n} = G$ such that either $A_{i - 1} ⊴ A_{i}$ or $A_{i} / {(A_{i - 1})}_{A_{i}}$ is 𝜎-primary for all $i = 1, \dots, n$ . We prove that if 𝐺 is a 𝜎-soluble group, then 𝜎-permutability is a transitive relation in 𝐺 if and only if $G^{N_{σ}} \cap A^{G} = G^{N_{σ}} \cap A_{G}$ for every 𝜎-subnormal subgroup 𝐴 of 𝐺.
Website
Google Scholar
- 28 August 2024
- Published by Walter de Gruyter GmbH in Journal of Group Theory
On 𝜎-permutable subgroups of 𝜎-soluble finite groups
by Zhigang Wang, A-Ming Liu, Vasily G. Safonov, Alexander N. Skiba
Let $σ = {σ_{i} ∣ i \in I}$ be some partition of the set of all primes and 𝐺 a finite group. Then 𝐺 is said to be 𝜎-full if 𝐺 has a Hall $σ_{i}$ -subgroup for all $i \in I$ and 𝜎-primary if 𝐺 is a $σ_{i}$ -group for some 𝑖. In addition, 𝐺 is 𝜎-soluble if every chief factor of 𝐺 is 𝜎-primary and 𝜎-nilpotent if 𝐺 is a direct product of 𝜎-primary groups. We write $G^{N_{σ}}$ for the 𝜎-nilpotent residual of 𝐺, which is the intersection of all normal subgroups 𝑁 of 𝐺 with 𝜎-nilpotent $G / N$ . A subgroup 𝐴 of 𝐺 is said to be 𝜎-permutable in 𝐺 provided 𝐺 is 𝜎-full and 𝐴 permutes with all Hall $σ_{i}$ -subgroups 𝐻 of 𝐺 (that is, $A H = H A$ ) for all 𝑖. And 𝐴 is 𝜎-subnormal in 𝐺 if there is a subgroup chain $A = A_{0} \leq A_{1} \leq \dots \leq A_{n} = G$ such that either $A_{i - 1} ⊴ A_{i}$ or $A_{i} / {(A_{i - 1})}_{A_{i}}$ is 𝜎-primary for all $i = 1, \dots, n$ . We prove that if 𝐺 is a 𝜎-soluble group, then 𝜎-permutability is a transitive relation in 𝐺 if and only if $G^{N_{σ}} \cap A^{G} = G^{N_{σ}} \cap A_{G}$ for every 𝜎-subnormal subgroup 𝐴 of 𝐺.

Show all