Separating cyclic subgroups in graph products of groups

JOURNAL OF ALGEBRA

卷:531

Article

Berlai, Federico¹  Ferov, Michal² 

[1] Univ Basque Country, Dept Math, Barrio Sarriena S-N, E-48940 Leioa, Spain

[2] Univ Technol Sydney, Sch Math & Phys Sci, POB 123 Broadway, Sydney, NSW 2007, Australia

关键词: Combinatorial group theory;    Profinite topology;    Separability properties of subgroups;    Cyclic subgroup separability;    Graph products;   

DOI  :  10.1016/j.jalgebra.2019.05.001

来源: Elsevier

【 摘 要 】

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. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free