RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Zametki, 2003, Volume 73, Issue 4, Pages 565–572 (Mi mz204)  

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

On Weakly Factorizable Groups

V. M. Levchuk

Krasnoyarsk State University

Abstract: Groups with complemented subgroups, which are also called completely factorizable groups, were studied by P. Hall, S. N. Chernikov, and N. V. Chernikova (Baeva). For complete factorizability, it is sufficient (Theorem 1) that each proper subgroup have a normal complement in some larger subgroup. A group is said to be weakly factorizable if each of its proper subgroups is complemented in some larger subgroup; the problem of describing finite groups with this property is posed (Question 8.31) in the “Kourovka Notebook”. Some properties of these groups are considered. The question is studied for Sylow $p$-subgroups of Chevalley-type groups of characteristic $p$. The main theorem, Theorem 2, establishes the weak factorizability of the Sylow $p$-subgroups in the symmetric and alternative groups and in the classical linear groups over fields of characteristic $p>0$, excluding the unitary groups of odd dimension $>p$.

DOI: https://doi.org/10.4213/mzm204

Full text: PDF file (209 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2003, 73:4, 529–535

Bibliographic databases:

UDC: 512.54
Received: 23.05.2001
Revised: 19.02.2002

Citation: V. M. Levchuk, “On Weakly Factorizable Groups”, Mat. Zametki, 73:4 (2003), 565–572; Math. Notes, 73:4 (2003), 529–535

Citation in format AMSBIB
\Bibitem{Lev03}
\by V.~M.~Levchuk
\paper On Weakly Factorizable Groups
\jour Mat. Zametki
\yr 2003
\vol 73
\issue 4
\pages 565--572
\mathnet{http://mi.mathnet.ru/mz204}
\crossref{https://doi.org/10.4213/mzm204}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1991902}
\zmath{https://zbmath.org/?q=an:1065.20035}
\transl
\jour Math. Notes
\yr 2003
\vol 73
\issue 4
\pages 529--535
\crossref{https://doi.org/10.1023/A:1023259204948}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000182776700028}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-1642462163}


Linking options:
  • http://mi.mathnet.ru/eng/mz204
  • https://doi.org/10.4213/mzm204
  • http://mi.mathnet.ru/eng/mz/v73/i4/p565

    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. V. M. Levchuk, A. G. Likharev, “Finite simple groups with complemented maximal subgroups”, Siberian Math. J., 47:4 (2006), 659–668  mathnet  crossref  mathscinet  zmath  isi
  • Математические заметки Mathematical Notes
    Number of views:
    This page:251
    Full text:92
    References:49
    First page:3

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