Separating cyclic subgroups in graph products of groups
We prove that the property of being cyclic subgroup separable, that is having all cyclic subgroups closed in the profinite topology, is preserved under forming graph products. Furthermore, we develop the tools to study the analogous question in the pro-p case. For a wide class of groups we show that...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universidad del País Vasco |
| Repositorio: | Addi. Archivo Digital para la Docencia y la Investigación |
| OAI Identifier: | oai:addi.ehu.eus:10810/72144 |
| Acceso en línea: | http://hdl.handle.net/10810/72144 |
| Access Level: | acceso abierto |
| Palabra clave: | combinatorial group theory profinite topology separability properties of groups cyclic subgroup separability graph product of groups |
| Sumario: | We prove that the property of being cyclic subgroup separable, that is having all cyclic subgroups closed in the profinite topology, is preserved under forming graph products. Furthermore, we develop the tools to study the analogous question in the pro-p case. For a wide class of groups we show that the relevant cyclic subgroups – which are called p-isolated – are closed in the pro-p topology of the graph product. In particular, we show that every p-isolated cyclic subgroup of a right-angled Artin group is closed in the pro-p topology, and we fully characterise such subgroups. |
|---|