On subgroups of Brin-Thompson groups $nV$

Sadayoshi Kojima; Xiaobing Sheng

On subgroups of Brin-Thompson groups $nV$

Group Theory 2026-05-27 v3 Geometric Topology

Authors: Sadayoshi Kojima , Xiaobing Sheng

Abstract

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

Cite

@article{arxiv.2603.18410,
  title  = {On subgroups of Brin-Thompson groups $nV$},
  author = {Sadayoshi Kojima and Xiaobing Sheng},
  journal= {arXiv preprint arXiv:2603.18410},
  year   = {2026}
}

Comments

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

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