Random Quotients of Free Products
Fuente:
arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913688448925696 |
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| author | Einstein, Eduard S, Suraj Krishna M Montee, MurphyKate Ng, Thomas Steenbock, Markus |
| author_facet | Einstein, Eduard S, Suraj Krishna M Montee, MurphyKate Ng, Thomas Steenbock, Markus |
| contents | We introduce a density model for random quotients of a free product of finitely generated groups. We prove that a random quotient in this model has the following properties with overwhelming probability: if the density is below $1/2$, the free factors embed into the random quotient and the random quotient is hyperbolic relative to the free factors. Further, there is a phase transition at $1/2$, with the random quotient being a finite group above this density. If the density is below $1/6$, the random quotient is cubulated relative to the free factors. Moreover, if the free factors are cubulated, then so is the random quotient. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_08630 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Random Quotients of Free Products Einstein, Eduard S, Suraj Krishna M Montee, MurphyKate Ng, Thomas Steenbock, Markus Group Theory 20F65, 20F67 We introduce a density model for random quotients of a free product of finitely generated groups. We prove that a random quotient in this model has the following properties with overwhelming probability: if the density is below $1/2$, the free factors embed into the random quotient and the random quotient is hyperbolic relative to the free factors. Further, there is a phase transition at $1/2$, with the random quotient being a finite group above this density. If the density is below $1/6$, the random quotient is cubulated relative to the free factors. Moreover, if the free factors are cubulated, then so is the random quotient. |
| title | Random Quotients of Free Products |
| topic | Group Theory 20F65, 20F67 |
| url | https://arxiv.org/abs/2502.08630 |