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From isolated subgroups to generic permutation representations
Let G be a countable group, Sub(G) be the (compact, metric) space of all subgroups of G with the Chabauty topology and Is(G) ⊆ Sub(G) be the collection of isolated points. We denote by X! the (Polish) group of all permutations of a countable set X. Then the following properties are equivalent: (i) Is(G) is dense in Sub(G); (ii) G admits a ‘generic permutation representation’. Namely, there exis...
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 1973
ISSN: 0026-2285
DOI: 10.1307/mmj/1029001103