# Sh:1117

- Paolini, G., & Shelah, S. (2017).
*Group metrics for graph products of cyclic groups*. Topology Appl.,**232**, 281–287. arXiv: 1705.02582 DOI: 10.1016/j.topol.2017.10.016 MR: 3720899 -
Abstract:

We complement the characterization of the graph products of cyclic groups G(\Gamma, {\mathfrak p}) admitting a Polish group topology of [9] with the following result. Let G = G(\Gamma, {\mathfrak p}), then the following are equivalent: [i] there is a metric on \Gamma which induces a separable topology in which E_{\Gamma} is closed; [ii] G(\Gamma, {\mathfrak p}) is embeddable into a Polish group; [iii] G(\Gamma, {\mathfrak p}) is embeddable into a non-Archimedean Polish group. We also construct left-invariant separable group ultrametrics for G = G(\Gamma, {\mathfrak p}) and \Gamma a closed graph on the Baire space, which is of independent interest. - published version (7p)

Bib entry

@article{Sh:1117, author = {Paolini, Gianluca and Shelah, Saharon}, title = {{Group metrics for graph products of cyclic groups}}, journal = {Topology Appl.}, fjournal = {Topology and its Applications}, volume = {232}, year = {2017}, pages = {281--287}, issn = {0166-8641}, doi = {10.1016/j.topol.2017.10.016}, mrclass = {54H11}, mrnumber = {3720899}, mrreviewer = {Michal Doucha}, doi = {10.1016/j.topol.2017.10.016}, note = {\href{https://arxiv.org/abs/1705.02582}{arXiv: 1705.02582}}, arxiv_number = {1705.02582} }