Separating cyclic subgroups in graph products of groups

Berlai, F; Ferov, M

Separating cyclic subgroups in graph products of groups

Berlai, F Ferov, M

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Field	Value	Language
dc.contributor.author	Berlai, F	en_US
dc.contributor.author	Ferov, M https://orcid.org/0000-0001-9108-1325	en_US
dc.date.accessioned	2020-03-16T03:51:35Z
dc.date.available	2020-03-16T03:51:35Z
dc.identifier.uri	http://hdl.handle.net/10453/139331
dc.description.abstract	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.	en_US
dc.relation	http://purl.org/au-research/grants/arc/DP160100486
dc.relation.isbasedon	10.1016/j.jalgebra.2019.05.001	en_US
dc.subject.classification	General Mathematics	en_US
dc.title	Separating cyclic subgroups in graph products of groups	en_US
dc.type	Journal Article
utslib.for	0101 Pure Mathematics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
utslib.copyright.status	closed_access

Abstract:

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.

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http://hdl.handle.net/10453/139331