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

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



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






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


Diskr. Mat., 2004, Volume 16, Issue 1, Pages 105–113 (Mi dm145)  

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

On new classes of conjugate injectors of finite groups

E. N. Zalesskaya


Abstract: In the study of the problem of existence and conjugacy in an arbitrary finite group it is known the Blessenohl–Laue result that in any finite group $G$ there exists a unique class of conjugate quasinilpotent injectors which are exactly the $\mathfrak N^*$-maximal subgroups of $G$ containing the generalised Fitting subgroup $F^*(G)$. In this paper, with the use of constructions of the Blessenohl–Laue and Gaschütz classes, we extend the Blessenohl–Laue result to the case of the Fitting class $\mathfrak F=\mathfrak H\mathfrak B$, where $\mathfrak H$ is a non-empty Fitting class and $\mathfrak B$ is a Blessenohl–Laue class, and thus we distinguish a new class of conjugate $\mathfrak F$-injectors in the classes $\mathfrak E$ of all finite groups and $\mathfrak S^{\pi}$ of all finite $\pi$-solvable groups respectively. Moreover, we prove that the $\mathfrak F$-injectors of the group $G$ are exactly all $\mathfrak F$-maximal subgroups of $G$, which contain its $\mathfrak F$-radical $G_{\mathfrak F}$. Special cases of such injectors are the injectors for many known Fitting classes. In particular, such injectors in the class $\mathfrak S$ of all finite solvable groups were described by B. Hartley, B. Fischer, W. Frantz, and P. Lockett.

DOI: https://doi.org/10.4213/dm145

Full text: PDF file (928 kB)
References: PDF file   HTML file

English version:
Discrete Mathematics and Applications, 2004, 14:2, 191–199

Bibliographic databases:

UDC: 512.542
Received: 03.04.2003

Citation: E. N. Zalesskaya, “On new classes of conjugate injectors of finite groups”, Diskr. Mat., 16:1 (2004), 105–113; Discrete Math. Appl., 14:2 (2004), 191–199

Citation in format AMSBIB
\Bibitem{Zal04}
\by E.~N.~Zalesskaya
\paper On new classes of conjugate injectors of finite groups
\jour Diskr. Mat.
\yr 2004
\vol 16
\issue 1
\pages 105--113
\mathnet{http://mi.mathnet.ru/dm145}
\crossref{https://doi.org/10.4213/dm145}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2069992}
\zmath{https://zbmath.org/?q=an:1065.20031}
\transl
\jour Discrete Math. Appl.
\yr 2004
\vol 14
\issue 2
\pages 191--199
\crossref{https://doi.org/10.1515/156939204872338}


Linking options:
  • http://mi.mathnet.ru/eng/dm145
  • https://doi.org/10.4213/dm145
  • http://mi.mathnet.ru/eng/dm/v16/i1/p105

    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. Goiko V.I., “In'ektory konechnykh grupp”, Vesnk Vtsebskaga dzyarzhainaga unversteta, 1:67 (2012), 5–11  elib
  • Number of views:
    This page:170
    Full text:92
    References:26
    First page:2

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