Stable subgroups of graph products
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911556969693184 |
|---|---|
| author | Balasubramanya, Sahana H Chesser, Marissa Kerr, Alice Mangahas, Johanna Trin, Marie |
| author_facet | Balasubramanya, Sahana H Chesser, Marissa Kerr, Alice Mangahas, Johanna Trin, Marie |
| contents | We extend the characterization of stable subgroups of right-angled Artin groups of Koberda, Mangahas and Taylor to the case of graph products of infinite groups. Specifically, we show that the stable subgroups of such graph products are exactly the subgroups that quasi-isometrically embed in the associated contact graph. Equivalently, they are the subgroups that satisfy a condition arising from the defining graph: a stable subgroup is an almost join-free subgroup. In particular, we generalize the equivalence between stable and purely loxodromic subgroups from Koberda, Mangahas and Taylor in the case where all torsion subgroups of the vertex groups are finite, and the equivalence between stable and infinite index Morse subgroups from Tran in the case where the defining graph is connected. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_11176 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stable subgroups of graph products Balasubramanya, Sahana H Chesser, Marissa Kerr, Alice Mangahas, Johanna Trin, Marie Group Theory 20F65, 20F67 We extend the characterization of stable subgroups of right-angled Artin groups of Koberda, Mangahas and Taylor to the case of graph products of infinite groups. Specifically, we show that the stable subgroups of such graph products are exactly the subgroups that quasi-isometrically embed in the associated contact graph. Equivalently, they are the subgroups that satisfy a condition arising from the defining graph: a stable subgroup is an almost join-free subgroup. In particular, we generalize the equivalence between stable and purely loxodromic subgroups from Koberda, Mangahas and Taylor in the case where all torsion subgroups of the vertex groups are finite, and the equivalence between stable and infinite index Morse subgroups from Tran in the case where the defining graph is connected. |
| title | Stable subgroups of graph products |
| topic | Group Theory 20F65, 20F67 |
| url | https://arxiv.org/abs/2511.11176 |