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arxiv: 1204.5939 · v6 · pith:P6GXRMKYnew · submitted 2012-04-26 · 🧮 math.DS · math.GR

Invariant random subgroups of the free group

classification 🧮 math.DS math.GR
keywords grouprandomfreeinvariantsubgroupcalledclosedcompact
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Let $G$ be a locally compact group. A random closed subgroup with conjugation-invariant law is called an {\em invariant random subgroup} or IRS for short. We show that each nonabelian free group has a large "zoo" of IRS's. This contrasts with results of Stuck-Zimmer which show that there are no non-obvious IRS's of higher rank semisimple Lie groups with property (T).

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