Invariant Random Subgroups

2020 ◽  
pp. 59-71
Author(s):  
Clara Löh
Keyword(s):  
Invariant Random Subgroups

Infinitely presented permutation stable groups and invariant random subgroups of metabelian groups

2021 ◽  
pp. 1-36
Author(s):  
ARIE LEVIT ◽  
ALEXANDER LUBOTZKY
Keyword(s):  
Ergodic Theorem ◽  
Abelian Groups ◽  
Wreath Products ◽  
Finitely Generated ◽  
Metabelian Groups ◽  
Amenable Groups ◽  
Pointwise Ergodic Theorem ◽  
Lamplighter Group ◽  
Invariant Random Subgroups

Abstract We prove that all invariant random subgroups of the lamplighter group L are co-sofic. It follows that L is permutation stable, providing an example of an infinitely presented such group. Our proof applies more generally to all permutational wreath products of finitely generated abelian groups. We rely on the pointwise ergodic theorem for amenable groups.

scholarly journals Invariant random subgroups of semidirect products

2018 ◽  
Vol 40 (2) ◽  
pp. 353-366
Author(s):  
IAN BIRINGER ◽  
LEWIS BOWEN ◽  
OMER TAMUZ
Keyword(s):  
Parabolic Subgroups ◽  
Semidirect Products ◽  
Invariant Random Subgroups

We study invariant random subgroups (IRSs) of semidirect products $G=A\rtimes \unicode[STIX]{x1D6E4}$. In particular, we characterize all IRSs of parabolic subgroups of $\text{SL}_{d}(\mathbb{R})$, and show that all ergodic IRSs of $\mathbb{R}^{d}\rtimes \text{SL}_{d}(\mathbb{R})$ are either of the form $\mathbb{R}^{d}\rtimes K$ for some IRS of $\text{SL}_{d}(\mathbb{R})$, or are induced from IRSs of $\unicode[STIX]{x1D6EC}\rtimes \text{SL}(\unicode[STIX]{x1D6EC})$, where $\unicode[STIX]{x1D6EC}<\mathbb{R}^{d}$ is a lattice.

Characters of inductive limits of finite alternating groups

2018 ◽  
Vol 40 (4) ◽  
pp. 1068-1082
Author(s):  
SIMON THOMAS
Keyword(s):  
Inductive Limit ◽  
Inductive Limits ◽  
Alternating Groups ◽  
Invariant Random Subgroups

If $G\ncong \operatorname{Alt}(\mathbb{N})$ is an inductive limit of finite alternating groups, then the indecomposable characters of $G$ are precisely the associated characters of the ergodic invariant random subgroups of $G$.

scholarly journals Invariant random subgroups over non-Archimedean local fields

2018 ◽  
Vol 372 (3-4) ◽  
pp. 1503-1544 ◽  
Author(s):  
Tsachik Gelander ◽  
Arie Levit
Keyword(s):  
Local Fields ◽  
Invariant Random Subgroups

Locally Compact Groups whose Ergodic or Minimal Actions are All Free

2018 ◽  
Vol 2020 (11) ◽  
pp. 3318-3340
Author(s):  
Adrien Le Boudec ◽  
Nicolás Matte Bon
Keyword(s):  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Invariant Random Subgroups

Abstract We construct locally compact groups with no nontrivial Invariant Random Subgroups and no nontrivial Uniformly Recurrent Subgroups.

scholarly journals Amenable invariant random subgroups

2016 ◽  
Vol 213 (1) ◽  
pp. 399-422 ◽  
Author(s):  
Uri Bader ◽  
Bruno Duchesne ◽  
Jean Lécureux ◽  
Phillip Wesolek
Keyword(s):  
Invariant Random Subgroups
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