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Universality of group embeddability

Authors: Filippo Calderoni and Luca Motto Ros
Journal: Proc. Amer. Math. Soc. 146 (2018), 1765-1780
MSC (2010): Primary 03E15
Published electronically: November 10, 2017
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Abstract: Working in the framework of Borel reducibility, we study various notions of embeddability between groups. We prove that the embeddability between countable groups, the topological embeddability between (discrete) Polish groups, and the isometric embeddability between separable groups with a bounded bi-invariant complete metric are all invariantly universal analytic quasi-orders. This strengthens some results from works by Williams and Ferenczi, Louveau and Rosendal.

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Additional Information

Filippo Calderoni
Affiliation: Dipartimento di matematica, \guillemotleft{Giuseppe Peano}\guillemotright, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy

Luca Motto Ros
Affiliation: Dipartimento di matematica, \guillemotleft{Giuseppe Peano}\guillemotright, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy

Keywords: Borel reducibility, countable groups, Polish groups, separable metric groups, group embeddability
Received by editor(s): February 13, 2017
Received by editor(s) in revised form: June 14, 2017
Published electronically: November 10, 2017
Communicated by: Heike Mildenberger
Article copyright: © Copyright 2017 American Mathematical Society

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