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Izv. Akad. Nauk SSSR Ser. Mat., 1980, Volume 44, Issue 2, Pages 288–308 (Mi izv1666)  

This article is cited in 5 scientific papers (total in 5 papers)

Tests for the nonsimplicity of factorable groups

L. S. Kazarin


Abstract: The following theorem is proved.
Theorem. Suppose that a finite group $G$ is the product of two subgroups $A$ and $B,$ where $B$ is of odd order. Let at least one of the following conditions be satisfied:
(a) $A$ is $2$-separable, and $(|A|,|B|)=1$.
(b) $A$ is $2$-nilpotent with a $2$-separable derived group, $B$ is nilpotent, and $(|A|,|B|)=1$.
(c) $A$ is supersolvable and $B$ is nilpotent.
\noindent Then $O(A)$ lies in $O(G)$.

Bibliography: 30 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1981, 16:2, 261–278

Bibliographic databases:

UDC: 519.44
MSC: 20D10
Received: 04.04.1979

Citation: L. S. Kazarin, “Tests for the nonsimplicity of factorable groups”, Izv. Akad. Nauk SSSR Ser. Mat., 44:2 (1980), 288–308; Math. USSR-Izv., 16:2 (1981), 261–278

Citation in format AMSBIB
\Bibitem{Kaz80}
\by L.~S.~Kazarin
\paper Tests for the nonsimplicity of factorable groups
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1980
\vol 44
\issue 2
\pages 288--308
\mathnet{http://mi.mathnet.ru/izv1666}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=571099}
\zmath{https://zbmath.org/?q=an:0462.20018|0429.20026}
\transl
\jour Math. USSR-Izv.
\yr 1981
\vol 16
\issue 2
\pages 261--278
\crossref{https://doi.org/10.1070/IM1981v016n02ABEH001304}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1981MK40900003}


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    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. Udo Preiser, “A characterization of PGL(2,q),q ODD”, Isr J Math, 43:2 (1982), 177  crossref  mathscinet  zmath  isi
    2. L. S. Kazarin, “Automorphisms, factorizations and theorems of Sylow-type theorems”, Math. USSR-Sb., 48:1 (1984), 183–192  mathnet  crossref  mathscinet  zmath
    3. Elsa Fisman, “Products ofSz(q) by other groups”, Arch Math, 42:2 (1984), 102  crossref  mathscinet  zmath  isi
    4. V. S. Monakhov, “On the Solvability of a Group with Commuting Subgroups”, Math. Notes, 93:3 (2013), 460–464  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    5. T. V. Tikhonenko, “Konechnye gruppy, soderzhaschie zadannuyu sistemu perestanovochnykh podgrupp”, PFMT, 2013, no. 2(15), 81–84  mathnet
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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