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Mat. Zametki, 1977, Volume 22, Issue 1, Pages 147–151 (Mi mz8035)  

Functionally complete groups

V. S. Anashin


Abstract: A group $G$ is called functionally complete if for an arbitrary natural number $n$ every mapping $f:G^n\to G$ can be realized by a «polynomial» in at most $n$ variables over the group $G$. We know that a group $G$ is functionally complete if and only if it is either trivial or a finite simple non-Abelian group [Ref. Zh. Mat. 9A174 (1975)]. In this article the ldquodegreerdquo of a polynomial and the connected notions of $n$-functional completeness, $(n;k_1,…,k_n)$-functional completeness, and strong functional completeness are introduced. It is shown that for $n>1$ these notions and the notion of functional completeness are equivalent, and apart from all finite simple non-Abelian groups, only the trivial group and groups of second order are 1-functionally complete.

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English version:
Mathematical Notes, 1977, 22:1, 571–574

Bibliographic databases:

UDC: 519.4
Received: 10.02.1976

Citation: V. S. Anashin, “Functionally complete groups”, Mat. Zametki, 22:1 (1977), 147–151; Math. Notes, 22:1 (1977), 571–574

Citation in format AMSBIB
\Bibitem{Ana77}
\by V.~S.~Anashin
\paper Functionally complete groups
\jour Mat. Zametki
\yr 1977
\vol 22
\issue 1
\pages 147--151
\mathnet{http://mi.mathnet.ru/mz8035}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=460452}
\zmath{https://zbmath.org/?q=an:0379.20026}
\transl
\jour Math. Notes
\yr 1977
\vol 22
\issue 1
\pages 571--574
\crossref{https://doi.org/10.1007/BF01147703}


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