Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports]
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Sib. Èlektron. Mat. Izv.:
Year:
Volume:
Issue:
Page:
Find






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


Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2020, Volume 17, Pages 1128–1136
DOI: https://doi.org/10.33048/semi.2020.17.085
(Mi semr1279)
 

Mathematical logic, algebra and number theory

On groups with a strongly embedded unitary subgroup

A. I. Sozutov

Siberian Federal University, 79, Svobodny ave., Krasnoyarsk, 660041, Russia
References:
Abstract: A proper subgroup $B$ of a group $G$ is called strongly embedded, if $2\in\pi(B)$ and $2\notin\pi(B \cap B^g)$ for every element $g \in G \setminus B $, and therefore $ N_G(X) \leq B$ for every $2$-subgroup $ X \leq B $. An element $a$ of a group $G$ is called finite, if for every $ g\in G $ the subgroup $ \langle a, a^g \rangle $ is finite.
In the paper, it is proved that a group with a finite element of order $4$ and a strongly embedded subgroup isomorphic to the Borel subgroup of $U_3(Q)$ over a locally finite field $Q$ of characteristic $2$ is locally finite and isomorphic to the group $U_3(Q)$.
Keywords: A strongly embedded subgroup of a unitary type, Borel subgroup, Cartan subgroup, involution, finite element.
Funding agency Grant number
Russian Science Foundation 19-71-10017
This work is supported by the Russian Science Foundation under grant No. 19-71-10017.
Received December 23, 2019, published August 21, 2020
Bibliographic databases:
Document Type: Article
UDC: 512.54
MSC: 20E42
Language: English
Citation: A. I. Sozutov, “On groups with a strongly embedded unitary subgroup”, Sib. Èlektron. Mat. Izv., 17 (2020), 1128–1136
Citation in format AMSBIB
\Bibitem{Soz20}
\by A.~I.~Sozutov
\paper On groups with a strongly embedded unitary subgroup
\jour Sib. \`Elektron. Mat. Izv.
\yr 2020
\vol 17
\pages 1128--1136
\mathnet{http://mi.mathnet.ru/semr1279}
\crossref{https://doi.org/10.33048/semi.2020.17.085}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000561108900001}
Linking options:
  • https://www.mathnet.ru/eng/semr1279
  • https://www.mathnet.ru/eng/semr/v17/p1128
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024