RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Guidelines for authors

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



J. Sib. Fed. Univ. Math. Phys.:
Year:
Volume:
Issue:
Page:
Find






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


J. Sib. Fed. Univ. Math. Phys., 2018, Volume 11, Issue 2, Pages 171–177 (Mi jsfu665)  

On intersection of primary subgroups in the group $\mathrm {Aut(F_4(2))}$

Viktor I. Zenkovab, Yakov N. Nuzhinc

a Institute of Mathematics and Mechanics UB RAS, Kovalevskoi, 16, Ekaterinburg, 620990
b Ural Federal University, Mira, 19, Ekaterinburg, 620990, Russia
c Institute of Mathematics and Computer Science, Siberian Federal University, Svobodny, 79, Krasnoyarsk, 660041, Russia

Abstract: It is proved that, in a finite group $G$ which is isomorphic to the group of automorphisms of the Chevalley group $F_4(2)$, there are only three possibilities for ordered pairs of primary subgroups $A$ and $B$ with condition: $A\cap B^g\ne 1$ for any $g\in G$. We describe all ordered pairs $(A,B)$ of such subgroups up to conjugacy in the group $G$ and in particular, we prove that $A$ and $B$ are $2$-groups.

Keywords: finite group, almost simple group, primary subgroup.

Funding Agency Grant Number
Russian Science Foundation 15-11-10025
Ministry of Education and Science of the Russian Federation 02.A03.21.0006,
Russian Foundation for Basic Research 16-01-00707_а
The first author was supported by the RNF (project 15-11-10025), Theorem 1, as well as agreements between the Russian Federation Ministry of Education and Science and Ural Federal University on 08/27/2013, number 02.A03.21.0006, Theorem 2. The work of the second author was supported by the RFBR (project 16-01-00707).


DOI: https://doi.org/10.17516/1997-1397-2018-11-2-171-177

Full text: PDF file (126 kB)
References: PDF file   HTML file

Bibliographic databases:

UDC: 512.542
Received: 20.05.2017
Received in revised form: 29.12.2017
Accepted: 20.01.2018
Language:

Citation: Viktor I. Zenkov, Yakov N. Nuzhin, “On intersection of primary subgroups in the group $\mathrm {Aut(F_4(2))}$”, J. Sib. Fed. Univ. Math. Phys., 11:2 (2018), 171–177

Citation in format AMSBIB
\Bibitem{ZenNuz18}
\by Viktor~I.~Zenkov, Yakov~N.~Nuzhin
\paper On intersection of primary subgroups in the group $\mathrm {Aut(F_4(2))}$
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2018
\vol 11
\issue 2
\pages 171--177
\mathnet{http://mi.mathnet.ru/jsfu665}
\crossref{https://doi.org/10.17516/1997-1397-2018-11-2-171-177}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000434678300005}


Linking options:
  • http://mi.mathnet.ru/eng/jsfu665
  • http://mi.mathnet.ru/eng/jsfu/v11/i2/p171

    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
  • Журнал Сибирского федерального университета. Серия "Математика и физика"
    Number of views:
    This page:183
    Full text:133
    References:10

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020