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, 2017, Issue 4(33), Pages 84–88 (Mi pfmt540)  

MATHEMATICS

Finite groups with $H_\sigma$-subnormally embedded subgroups

D. A. Sinitsaa, A. N. Skibaa, W. Guob, Chi Zhangb

a F. Scorina Gomel State University
b University of Science and Technology of China, Hefei

Abstract: Пусть $G$ be a finite group. Let $\sigma=\{\sigma_i| i\in I\}$ be a partition of the set of all primes $\mathbb{P}$ and $n$ an integer. We write $\sigma(n)=\{\sigma_i |\sigma_i\cap \pi(n)\ne\varnothing\}$, $\sigma(G)=\sigma(|G|)$. A set $\mathcal{H}$ of subgroups of $G$ is said to be a complete Hall $\sigma$-set of $G$ if every member of $\mathcal{H}\setminus\{1\}$ is a Hall $\sigma_i$-subgroup of $G$ for some $\sigma_i$ and $\mathcal{H}$ contains exact one Hall $\sigma_i$-subgroup of $G$ for every $\sigma_i\in\sigma(G)$. A subgroup $A$ of $G$ is called a $\sigma$-Hall subgroup of $G$ if $\sigma(|A|)\cap\sigma(|G:A|)=\varnothing$. We say that a subgroup $A$ of $G$ is $H_\sigma$-subnormally embedded in $G$ if $A$ is a $\sigma$-Hall subgroup of some $\sigma$-subnormal subgroup of $G$.

Keywords: finite group, $\sigma$-subnormal subgroup, $\sigma$-permutable subgroup, $\sigma$-Hall subgroup, $H_\sigma$-subnormally embedded subgroup.

Full text: PDF file (351 kB)
References: PDF file   HTML file
UDC: 512.542
Received: 08.10.2017

Citation: D. A. Sinitsa, A. N. Skiba, W. Guo, Chi Zhang, “Finite groups with $H_\sigma$-subnormally embedded subgroups”, PFMT, 2017, no. 4(33), 84–88

Citation in format AMSBIB
\Bibitem{SinSkiGuo17}
\by D.~A.~Sinitsa, A.~N.~Skiba, W.~Guo, Chi~Zhang
\paper Finite groups with $H_\sigma$-subnormally embedded subgroups
\jour PFMT
\yr 2017
\issue 4(33)
\pages 84--88
\mathnet{http://mi.mathnet.ru/pfmt540}


Linking options:
  • http://mi.mathnet.ru/eng/pfmt540
  • http://mi.mathnet.ru/eng/pfmt/y2017/i4/p84

    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:148
    Full text:33
    References:27

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