Universality of group embeddability

Calderoni, Filippo; Motto Ros, Luca

doi:10.1090/proc/13857

Universality of group embeddability
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by Filippo Calderoni and Luca Motto Ros PDF

Proc. Amer. Math. Soc. 146 (2018), 1765-1780 Request permission

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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