Universal Groups of Intermediate Growth and Their Invariant Random Subgroups

Benli, Mustafa Gokhan; Grigorchuk, Rostislav; Nagnibeda, Tatiana; Nagnibeda, Tat'yana V

doi:10.4213/faa3205

Funktsional. Anal. i Prilozhen.

2015

DOI: 10.4213/faa3205

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Universal Groups of Intermediate Growth and Their Invariant Random Subgroups

Mustafa Gokhan Benli¹,

Rostislav Grigorchuk²,

Tatiana Nagnibeda³

et al.

Abstract: В работе приведены примеры групп промежуточного роста с $2^{\aleph_0}$ эргодическими непрерывными инвариантными случайными подгруппами. Эти примеры - универсальные группы, ассоциированные с некоторым семейством групп промежуточного роста.

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2016

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Ergodic decomposition of group actions on rooted trees

Grigorchuk

Savchuk

2016

Proc. Steklov Inst. Math.

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We prove a general result about the decomposition on ergodic components of group actions on boundaries of spherically homogeneous rooted trees. Namely, we identify the space of ergodic components with the boundary of the orbit tree associated with the action, and show that the canonical system of ergodic invariant probability measures coincides with the system of uniform measures on the boundaries of minimal invariant subtrees of the tree.A special attention is given to the case of groups generated by finite automata. Few examples, including the lamplighter group, Sushchansky group, and the, so called, Universal group are considered in order to demonstrate applications of the theorem.

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Ergodic decomposition of group actions on rooted trees

Grigorchuk

Savchuk

2016

Proc. Steklov Inst. Math.

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show abstract

Ergodic Decomposition of Group Actions on Rooted Trees

Grigorchuk

Savchuk

2016

Тр. Мат. ин-та РАН

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Universal Groups of Intermediate Growth and Their Invariant Random Subgroups

Cited by 2 publications

References 19 publications

Ergodic decomposition of group actions on rooted trees

Ergodic decomposition of group actions on rooted trees

Ergodic Decomposition of Group Actions on Rooted Trees

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