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Mat. Vopr. Kriptogr., 2019, Volume 10, Issue 4, Pages 53–65 (Mi mvk307)  

On the existence of non-negative bases in subgroups of free groups of Schreier varieties

I. A. Kruglova, I. V. Cherednikb

a Academy of Cryptography of Russian Federation, Moscow
b "Certification Research Center", LCC, Moscow

Abstract: We show that a subgroup $H$ of a free group $F(X)$ has a non-negative (with respect to $X$) basis if and only if $H$ is generated by the set of all its non-negative (with respect to $X$) elements. A similar result is proved for subgroups of free Abelian groups.

Key words: non-negative basis of a subgroup, free groups, free Abelian groups, Schreier varieties of groups.

DOI: https://doi.org/10.4213/mvk307

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UDC: 512.543.1+512.543.2
Received 30.V.2016, 03.X.2019

Citation: I. A. Kruglov, I. V. Cherednik, “On the existence of non-negative bases in subgroups of free groups of Schreier varieties”, Mat. Vopr. Kriptogr., 10:4 (2019), 53–65

Citation in format AMSBIB
\Bibitem{KruChe19}
\by I.~A.~Kruglov, I.~V.~Cherednik
\paper On the existence of non-negative bases in subgroups of free groups of Schreier varieties
\jour Mat. Vopr. Kriptogr.
\yr 2019
\vol 10
\issue 4
\pages 53--65
\mathnet{http://mi.mathnet.ru/mvk307}
\crossref{https://doi.org/10.4213/mvk307}


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