Problemy Fiziki, Matematiki i Tekhniki (Problems of Physics, Mathematics and Technics)
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



PFMT:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


PFMT, 2020, Issue 1(42), Pages 65–73 (Mi pfmt698)  

MATHEMATICS

Finite groups with generalized $\sigma$-subnormal and $\sigma$-permutable subgroups

N. M. Adarchenko, A. N. Skiba

F. Scorina Gomel State University

Abstract: Throughout this paper, all groups are finite and $G$ always denotes a finite group. We say that a subgroup $H$ of $G$ is nearly modular in $G$ if either $A$ is normal in $G$ or $H_g\ne H^G$ and every chief factor $H/K$ of $G$ between $H_G$ and $H^G$ is nearly central in $G$, that is, $|H/K||GC_G(H/K)|$ divides $pq$ for some primes $p$ and $q$. We say that a subgroup $A$ of $G$ is:
(i) nearly $\sigma$-subnormal in $G$ if $A=\langle L,T\rangle$, where $L$ is a nearly modular subgroup and $T$ is a $\sigma$-subnormal subgroup of $G$;
(ii) nearly $\sigma$-permutable in $G$ if $A=\langle L,T\rangle$, where $L$ is a nearly modular subgroup and $T$ is a $\sigma$-permutable subgroup of $G$.
(iii) weakly $\sigma$-permutable in $G$ if there are a nearly $\sigma$-permutable subgroup $S$ and a subgroup $T$ of $G$ such that $G=HT$ and $H\cap T\leqslant S\leqslant H$.
In the given paper, we study finite groups with some systems of nearly $\sigma$-subnormal, nearly $\sigma$-permutable and weakly $\sigma$-permutable subgroups. Some known results are generalized.

Keywords: finite group, $n$-maximal subgroup, nearly $\sigma$-subnormal subgroup, nearly $\sigma$-permutable subgroup, $\sigma$-nearly nilpotent group.

Full text: PDF file (435 kB)
References: PDF file   HTML file
UDC: 512.54
MSC: 20D10, 20D20, 20D30, 20D35
Received: 17.12.2019
Language:

Citation: N. M. Adarchenko, A. N. Skiba, “Finite groups with generalized $\sigma$-subnormal and $\sigma$-permutable subgroups”, PFMT, 2020, no. 1(42), 65–73

Citation in format AMSBIB
\Bibitem{AdaSki20}
\by N.~M.~Adarchenko, A.~N.~Skiba
\paper Finite groups with generalized $\sigma$-subnormal and $\sigma$-permutable subgroups
\jour PFMT
\yr 2020
\issue 1(42)
\pages 65--73
\mathnet{http://mi.mathnet.ru/pfmt698}


Linking options:
  • http://mi.mathnet.ru/eng/pfmt698
  • http://mi.mathnet.ru/eng/pfmt/y2020/i1/p65

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Проблемы физики, математики и техники
    Number of views:
    This page:104
    Full text:29
    References:2

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021