Geodesic
On the existence of non-negative bases in subgroups of free groups of Schreier varieties
Matematičeskie voprosy kriptografii, Tome 10 (2019), pp. 53-65.

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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. 
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I. A. Kruglov; I. V. Cherednik. On the existence of non-negative bases in subgroups of free groups of Schreier varieties. Matematičeskie voprosy kriptografii, Tome 10 (2019), pp. 53-65. http://geodesic.mathdoc.fr/item/MVK_2019_10_a3/

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