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Trudy Inst. Mat. i Mekh. UrO RAN, 2015, Volume 21, Number 1, Pages 122–127 (Mi timm1148)  

This article is cited in 4 scientific papers (total in 4 papers)

On the existence of complements for residuals of finite groups

S. F. Kamornikova, O. L. Shemetkovab

a Gomel Branch of International Institute of Labor and Social Relations
b Plekhanov Russian State University of Economics, Moscow

Abstract: L.A. Shemetkov's theorem on the complementability of the $\mathfrak{F}$-residual of a finite group is developed in the article. For a local Fitting formation $\mathfrak{F}$, it is proved that, if a group $G$ is representable in the form $G=AB$, where $A$ and $B$ are subnormal subgroups of $G$, the subgroups $A^\mathfrak{F}$ and $B^\mathfrak{F}$ are $\pi(\mathfrak{F})$-solvable and normal in $G$, and Sylow $p$-subgroups of $A^\mathfrak{F}$ and $B^\mathfrak{F}$ are abelian for every $p \in \pi(\mathfrak{F})$, then every $\mathfrak{F}$-normalizer of $G$ is the complement for an $\mathfrak{F}$-residual of $G$.

Keywords: finite group; subnormal subgroup; formation; residual; complement; local Fitting formation.

Full text: PDF file (136 kB)
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Bibliographic databases:
UDC: 512.542
Received: 30.06.2014

Citation: S. F. Kamornikov, O. L. Shemetkova, “On the existence of complements for residuals of finite groups”, Trudy Inst. Mat. i Mekh. UrO RAN, 21, no. 1, 2015, 122–127

Citation in format AMSBIB
\Bibitem{KamShe15}
\by S.~F.~Kamornikov, O.~L.~Shemetkova
\paper On the existence of complements for residuals of finite groups
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2015
\vol 21
\issue 1
\pages 122--127
\mathnet{http://mi.mathnet.ru/timm1148}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3379609}
\elib{https://elibrary.ru/item.asp?id=23137978}


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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. S. F. Kamornikov, O. L. Shemetkova, “O dopolnenii koradikala konechnoi gruppy”, PFMT, 2017, no. 4(33), 58–64  mathnet
    2. V. A. Vedernikov, M. M. Sorokina, “The $\mathfrak F^\omega$-normalizers of finite groups”, Siberian Math. J., 58:1 (2017), 49–62  mathnet  crossref  crossref  isi  elib  elib
    3. X. Yi, S. F. Kamornikov, “On Shemetkov's theorem about the complementedness of the residual”, Siberian Math. J., 59:2 (2018), 276–282  mathnet  crossref  crossref  isi  elib
    4. S. F. Kamornikov, O. L. Shemetkova, “O dopolneniyakh koradikala v rasshireniyakh konechnykh grupp”, PFMT, 2018, no. 3(36), 80–83  mathnet
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