From isolated subgroups to generic permutation representations Academic Article uri icon

abstract

  • Let be a countable group, be the (compact, metric) space of all subgroups of with the Chabauty topology and be the collection of isolated points. We denote by the (Polish) group of all permutations of a countable set. Then the following properties are equivalent:(i) is dense in;(ii) admits a 'generic permutation representation'. Namely, there exists some such that the collection of permutation representations is co-meager in. We call groups satisfying these properties solitary. Examples of solitary groups include finitely generated locally extended residually finite groups and groups with countably many subgroups.

publication date

  • December 1, 2016