Separating cyclic subgroups in graph products of groups

Title: Separating cyclic subgroups in graph products of groups
Creator: Berlai, Federico; Ferov, Michal
Relation: Journal of Algebra Vol. 531, Issue August 2019, p. 19-56
Publisher Link: http://dx.doi.org/10.1016/j.jalgebra.2019.05.001
Publisher: Academic Press
Resource Type: journal article
Date: 2019
Description: 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.
Subject: combinatorial group theory; profinite topology; separability properties of subgroups; cyclic subgroup separability; graph products
Identifier: http://hdl.handle.net/1959.13/1437369
Identifier: uon:40327
Identifier: ISSN:0021-8693
Language: eng
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