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Algebra i Logika. Sem., 1967, Volume 6, Number 3, Pages 9–11 (Mi al1102)  

The variety generated of the finite group

Yu. M. Gorčakov


Abstract: The purpose of this paper is to give the simple proof of the following theorem (if [I]): the product $\mathfrak{N}\mathfrak{M}$ of the non-trivial varieties $\mathfrak{N}$ and $\mathfrak{M}$ is generated by the finite group if and only if
a) $\mathfrak{N}$ and $\mathfrak{M}$ has non zero coprime exponents and
b) $\mathfrak{N}$ consists of the nilpotent groups and $\mathfrak{M}$ consists of the abelian groups.
References

1. A. L. Šmelkin, The wreath products and the group varieties, Isvestia Akademee Nauk USSR, ser.math., 29,N I (1965), 149–170.

Full text: PDF file (95 kB)

Bibliographic databases:
Received: 10.04.1967

Citation: Yu. M. Gorčakov, “The variety generated of the finite group”, Algebra i Logika. Sem., 6:3 (1967), 9–11

Citation in format AMSBIB
\Bibitem{Gor67}
\by Yu.~M.~Gor{\v{c}}akov
\paper The variety generated of the finite group
\jour Algebra i Logika. Sem.
\yr 1967
\vol 6
\issue 3
\pages 9--11
\mathnet{http://mi.mathnet.ru/al1102}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=0218430}


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