Searcharxiv⌕ Search

arXiv subjects

Alexander N. Skiba

Publications and source records attributed to Alexander N. Skiba.

25 records · Page 2Linked to original sources
arXiv2014

On one generalization of finite $\frak U$-critical groups

A proper subgroup $H$ of a group $G$ is said to be: $\Bbb{P}$-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 prime for $i=1,...,n$; $\Bbb{P}$-abnormal in $G$ if for every two subgroups $K\leq L$ of $G$, where $H\leq K$, $|L:K|$ is not a prime. In this paper we describe finite groups in which every non-identity subgroup is either $\Bbb{P}$-subnormal or $\Bbb{P}$-abnormal.

math.GR↗
arXiv2013

Some new characterizations of $PST$-groups

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 $H$ permutes with $B$ and with every subgroup (respectively with every Sylow subgroup) $A$ of $B$ such that $(|H|, |A|)=1$. In this paper we analyze the influence of $S$-quasipermutable and quasipermutable subgroups on the structure of $G$. As an application, we give new characterizations of soluble $PST$-groups.

math.GR↗
arXiv2012

On the intersection of the $\cal F$-maximal subgroups and the generalized ${\cal F}$-hypercentre of a finite group

Let $\cal F$ be a class of groups. A chief factor $H/K$ of a group $G$ is called \emph{${\cal F}$-central in $G$} provided $(H/K)\rtimes (G/C_{G}(H/K)) \in {\cal F}$. We write $Z_{π{\cal F}}(G)$ to denote the product of all normal subgroups of $G$ whose $G$-chief factors of order divisible by at least one prime in $π$ are $\cal F$-central. We call $Z_{π{\cal F}}(G)$ the $π{\cal F}$-hypercentre of $G$. A subgroup $U$ of a group $G$ is called \emph{$\cal F$-maximal} in $G$ provided that (a) $U\in {\cal F}$, and (b) if $U\leq V\leq G$ and $V\in {\cal F}$, then $U=V$. In this paper we study the properties of the intersection of all $\cal F$-maximal subgroups of a finite group. In particular, we analyze the condition under which $Z_{π{\cal F}}(G)$ coincides with the intersection of all $\cal F$-maximal subgroups of $G$.

math.GR↗
arXiv2011

On a question of L.A. Shemetkov concerning the intersection of $\cal F$-maximal subgroups of finite groups

We investigate the influence of the intersection of the $\cal F$-maximal subgroups on the structure of a finite group. In particular, answering a question of L.A Shemetkov we give conditions under which a hereditary saturated formation $\cal F$ has a property that for any finite group $G$, the ${\cal F}$-hypercentre of $G$ coincides with the intersection of all $\cal F$-maximal subgroups of $G$.

math.GR↗