Matematičeskie voprosy kriptografii, Tome 10 (2019) no. 4, pp. 53-65
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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) no. 4, pp. 53-65. http://geodesic.mathdoc.fr/item/MVK_2019_10_4_a3/
@article{MVK_2019_10_4_a3,
author = {I. A. Kruglov and I. V. Cherednik},
title = {On the existence of non-negative bases in subgroups of free groups of {Schreier} varieties},
journal = {Matemati\v{c}eskie voprosy kriptografii},
pages = {53--65},
year = {2019},
volume = {10},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MVK_2019_10_4_a3/}
}
TY - JOUR
AU - I. A. Kruglov
AU - I. V. Cherednik
TI - On the existence of non-negative bases in subgroups of free groups of Schreier varieties
JO - Matematičeskie voprosy kriptografii
PY - 2019
SP - 53
EP - 65
VL - 10
IS - 4
UR - http://geodesic.mathdoc.fr/item/MVK_2019_10_4_a3/
LA - ru
ID - MVK_2019_10_4_a3
ER -
%0 Journal Article
%A I. A. Kruglov
%A I. V. Cherednik
%T On the existence of non-negative bases in subgroups of free groups of Schreier varieties
%J Matematičeskie voprosy kriptografii
%D 2019
%P 53-65
%V 10
%N 4
%U http://geodesic.mathdoc.fr/item/MVK_2019_10_4_a3/
%G ru
%F MVK_2019_10_4_a3
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.
