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Sibirsk. Mat. Zh., 2008, Volume 49, Number 6, Pages 1411–1419 (Mi smj1928)  

This article is cited in 2 scientific papers (total in 2 papers)

Maximal subclasses of local fitting classes

N. V. Savel'eva, N. T. Vorob'ev

Vitebsk State University named after P. M. Masherov

Abstract: A Fitting class $\mathfrak F$ is said to be $\pi$-maximal if $\mathfrak F$ is an inclusion maximal subclass of the Fitting class $\mathfrak S_\pi$ of all finite soluble $\pi$-groups. We prove that $\mathfrak F$ is a $\pi$-maximal Fitting class exactly when there is a prime $p\in\pi$ such that the index of the $\mathfrak F$-radical $G_\mathfrak F$ in $G$ is equal to 1 or $p$ for every $\pi$-subgroup of $G$. Hence, there exist maximal subclasses in a local Fitting class. This gives a negative answer to Skiba's conjecture that there are no maximal Fitting subclasses in a local Fitting class (see [1, Question 13.50]).

Keywords: Fitting class, maximal Fitting subclass, local Fitting class, $\mathfrak F$-radical, Lockett class, Lausch group, Fitting pair.

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English version:
Siberian Mathematical Journal, 2008, 49:6, 1124–1130

Bibliographic databases:

UDC: 512.542
Received: 25.04.2007

Citation: N. V. Savel'eva, N. T. Vorob'ev, “Maximal subclasses of local fitting classes”, Sibirsk. Mat. Zh., 49:6 (2008), 1411–1419; Siberian Math. J., 49:6 (2008), 1124–1130

Citation in format AMSBIB
\Bibitem{SavVor08}
\by N.~V.~Savel'eva, N.~T.~Vorob'ev
\paper Maximal subclasses of local fitting classes
\jour Sibirsk. Mat. Zh.
\yr 2008
\vol 49
\issue 6
\pages 1411--1419
\mathnet{http://mi.mathnet.ru/smj1928}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2499110}
\transl
\jour Siberian Math. J.
\yr 2008
\vol 49
\issue 6
\pages 1124--1130
\crossref{https://doi.org/10.1007/s11202-008-0108-7}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000261792400017}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-57749191052}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. N. V. Savelyeva, “Maximal fitting subclasses of the class of all finite $\pi$-groups”, Siberian Math. J., 54:1 (2013), 137–143  mathnet  crossref  mathscinet  isi
    2. N. T. Vorob'ev, A. V. Martsinkevich, “Finite $\pi$-groups with normal injectors”, Siberian Math. J., 56:4 (2015), 624–630  mathnet  crossref  crossref  mathscinet  isi  elib
  • Сибирский математический журнал Siberian Mathematical Journal
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