Amenability versus non-exactness of dense subgroups of a compact group

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Abstract

Given a countable residually finite group, we construct a compact group K and two elements w and u of K with the following properties: The group generated by w and u3 is amenable, the group generated by w and u contains a copy of the given group, and these two groups are dense in K. By combining it with a construction of non-exact groups that are locally embeddable into finite (LEF) by Osajda and Arzhantseva–Osajda and formation of diagonal products, we construct an example for which the latter dense group is non-exact. Our proof employs approximations in the space of marked groups of LEF groups.

Original languageEnglish
Pages (from-to)592-622
Number of pages31
JournalJournal of the London Mathematical Society
Volume100
Issue number2
DOIs
Publication statusPublished - 2019 Oct 1

Keywords

  • 20D06 (secondary)
  • 20F69 (primary)

ASJC Scopus subject areas

  • Mathematics(all)

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