RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zap. Nauchn. Sem. POMI:
Year:
Volume:
Issue:
Page:
Find






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


Zap. Nauchn. Sem. LOMI, 1979, Volume 86, Pages 34–39 (Mi znsl1820)  

This article is cited in 1 scientific paper (total in 1 paper)

Self-normalizing nilpotent subgroups of the full linear group over a finite field

N. A. Vavilov


Abstract: It has been proved (Ref. Zh. Mat., 1977, 4A170) that in the full linear group $GL(n,q)$, $n=2,3$, over a finite field of $q$ elements, $q$ odd or $q=2$, the only self-normalizing nilpotent subgroups are the normalizers of Sylow 2-subgroups and that for even $q>2$ there are no such subgroups. In the present note it is deduced from results of D. A. Suprunenko and R. F. Apatenok (Ref. Zh. Mat., 1960, 13586; 1962, 9A150) that this is true for any $n$.

Full text: PDF file (566 kB)

English version:
Journal of Soviet Mathematics, 1981, 17:4, 1963–1967

Bibliographic databases:

UDC: 519.46

Citation: N. A. Vavilov, “Self-normalizing nilpotent subgroups of the full linear group over a finite field”, Algebraic numbers and finite groups, Zap. Nauchn. Sem. LOMI, 86, "Nauka", Leningrad. Otdel., Leningrad, 1979, 34–39; J. Soviet Math., 17:4 (1981), 1963–1967

Citation in format AMSBIB
\Bibitem{Vav79}
\by N.~A.~Vavilov
\paper Self-normalizing nilpotent subgroups of the full linear group over a~finite field
\inbook Algebraic numbers and finite groups
\serial Zap. Nauchn. Sem. LOMI
\yr 1979
\vol 86
\pages 34--39
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl1820}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=535478}
\zmath{https://zbmath.org/?q=an:0459.20043|0422.20034}
\transl
\jour J. Soviet Math.
\yr 1981
\vol 17
\issue 4
\pages 1963--1967
\crossref{https://doi.org/10.1007/BF01465453}


Linking options:
  • http://mi.mathnet.ru/eng/znsl1820
  • http://mi.mathnet.ru/eng/znsl/v86/p34

    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

    This publication is cited in the following articles:
    1. E. P. Vdovin, “Karterovy podgruppy konechnykh grupp”, Matem. tr., 11:2 (2008), 20–106  mathnet  mathscinet  elib; E. P. Vdovin, “Carter subgroups of finite groups”, Siberian Adv. Math., 19:1 (2009), 24–74  crossref  elib
  • Записки научных семинаров ПОМИ
    Number of views:
    This page:95
    Full text:31

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2017