scholarly journals The Shannon–McMillan–Breiman theorem beyond amenable groups

2021 ◽  
Vol 65 (4) ◽  
Author(s):  
Amos Nevo ◽  
Felix Pogorzelski
Keyword(s):  
Amenable Groups

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 Bohr Sets in Triple Products of Large Sets in Amenable Groups

2018 ◽  
Vol 25 (3) ◽  
pp. 923-936
Author(s):  
Michael Björklund ◽  
John T. Griesmer
Keyword(s):  
Amenable Groups ◽  
Large Sets

On a construction of unitary cocycles and the representation theory of amenable groups

1983 ◽  
Vol 3 (1) ◽  
pp. 129-133 ◽  
Author(s):  
Colin E. Sutherland
Keyword(s):  
Representation Theory ◽  
Probability Space ◽  
Amenable Group ◽  
Unitary Representations ◽  
Intertwining Operators ◽  
Type I ◽  
Amenable Groups

AbstractIf K is a countable amenable group acting freely and ergodically on a probability space (Γ, μ), and G is an arbitrary countable amenable group, we construct an injection of the space of unitary representations of G into the space of unitary 1-cocyles for K on (Γ, μ); this injection preserves intertwining operators. We apply this to show that for many of the standard non-type-I amenable groups H, the representation theory of H contains that of every countable amenable group.

scholarly journals The Myhill property for strongly irreducible subshifts over amenable groups

2010 ◽  
Vol 165 (2) ◽  
pp. 155-172 ◽  
Author(s):  
Tullio Ceccherini-Silberstein ◽  
Michel Coornaert
Keyword(s):  
Amenable Groups ◽  
Strongly Irreducible
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