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JOURNALS // Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports] // Archive

Sib. Èlektron. Mat. Izv., 2021 Volume 18, Issue 2, Pages 1757–1770 (Mi semr1476)

Mathematical logic, algebra and number theory

Locally free subgroups of one-relator groups

A. I. Budkin

Altai State University, 61, Lenina ave., Barnaul, 656049, Russia

Abstract: 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.

UDC: 512.54

MSC: 20F05

Received March 9, 2021, published December 30, 2021

Language: English

DOI: 10.33048/semi.2021.18.135



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© Steklov Math. Inst. of RAS, 2025