Some obstructions on the subgroups of the Brin-Thompson groups and a selection of twisted Brin-Thompson groups
Xiaobing Sheng

TL;DR
This paper investigates obstructions to subgroups in higher-dimensional and twisted Brin-Thompson groups, revealing similarities to Thompson's group V and excluding certain Baumslag-Solitor groups as subgroups.
Contribution
It extends subgroup obstruction results from Thompson's group V to higher-dimensional and twisted Brin-Thompson groups, identifying key similarities and differences.
Findings
Obstructions on torsion subgroups are similar to those in Thompson's V
Certain Baumslag-Solitor groups are excluded as subgroups
Restrictions on subgroups diminish in the larger class V
Abstract
Motivated by Burillo, Cleary and Roever's summary on obstructions of subgroups of Thompson's group we explored the higher dimensional version of the groups, Brin-Thompson groups and a class of infinite dimensional Brin-Thompson groups and an easy class of the twisted version of the Brin-Thompson groups with some certain condition. We found that they have similar obstructions as Thompson's group on the torsion subgroups and a selection of the interesting Baumslag-Solitor groups are excluded as the subgroups of and We also discuss a little on the group an even larger class relaxing some of the "finiteness condition" and observe that some of the restrictions on subgroups disappear.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Finite Group Theory Research
