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Algebra i Logika. Sem., 1967, Volume 6, Number 3, Pages 25–30 (Mi al1104)  

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

Multinilponent groups

Yu. M. Gorčakov


Abstract: Let $\mathfrak{N}_k$ be the variety of all nilpoteht groups of class $\leqslant k$. From the varieties $\mathfrak{N}_{k_1},…,\mathfrak{N}_{k_s}$ the variety $\mathfrak{N}$ is constructed by intersections and multiplications. Any group of variety $\mathfrak{N}$ is called the multipolynilpotent group. In this note is proved Malcev's hypothesis: free multipolynilpotent group $N$ satisfies the following conditions:
  • $\bigcap\limits_n\gamma_n(N)=\{1\}$, where $\gamma_n(N)$ is $n$ member of descending central series of the group $N$, $n$ is natural number,
  • factors $\gamma_n(N)/\gamma_{n+1}(N)$ are free abelian groups.


Full text: PDF file (195 kB)

Bibliographic databases:
Received: 07.05.1967

Citation: Yu. M. Gorčakov, “Multinilponent groups”, Algebra i Logika. Sem., 6:3 (1967), 25–30

Citation in format AMSBIB
\Bibitem{Gor67}
\by Yu.~M.~Gor{\v{c}}akov
\paper Multinilponent groups
\jour Algebra i Logika. Sem.
\yr 1967
\vol 6
\issue 3
\pages 25--30
\mathnet{http://mi.mathnet.ru/al1104}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=0219619}


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  • http://mi.mathnet.ru/eng/al1104
  • http://mi.mathnet.ru/eng/al/v6/i3/p25

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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. V. D. Mazurov, “Solved problems in the Kourovka Notebook”, Russian Math. Surveys, 46:5 (1991), 137–182  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. L. A. Bokut, “Early history of the theory of rings in Novosibirsk”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2017, no. 2, 5–23  mathnet  mathscinet
  • Алгебра и логика Algebra and Logic
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