On subgroups of Brin-Thompson groups $nV$

Abstract

We prove that the Brin-Thompson group $nV$ is torsion locally finite for $n\ge 1$ which is known only when $n=1$, and $nV$ contains continuum many copies of the additive group of the rationals $\mathbb{Q}$ for $n\ge 2$ which is known to be false for the $n=1$ case.

The second claim has been upgraded, 18 pages, 9 figures, Section.5 is deleted. Typos are fixed and references are revised