Geodesic
Locally free subgroups of one-relator groups
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1757-1770

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Let $G_1=\langle x_1,\dots x_s; [x_1,x_{n+1}][x_{2},x_{n+2}]\dots [x_{n},x_{2n}]S\rangle $, $G_2=\langle a, x_1,\dots ,x_s; [a,x_1][a,x_2]\dots [a,x_n]S \rangle $ be one-relator groups. We find conditions on $S$ and $n$ under which the normal closure of each $(n-1)$-generated subgroup of $G_1$ and of each 3-generated subgroup of $G_2$ is locally free.
Keywords: one-relator group, locally free group, $n$-free group. 
@article{SEMR_2021_18_2_a17,
     author = {A. I. Budkin},
     title = {Locally free subgroups of one-relator groups},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1757--1770},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a17/}
}
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A. I. Budkin. Locally free subgroups of one-relator groups. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1757-1770. http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a17/