Strong amenability and the infinite conjugacy class property

Strong amenability and the infinite conjugacy class property

A group is said to be strongly amenable if each of its proximal topological actions has a fixed point. We show that a finitely generated group is strongly amenable if and only if it is virtually nilpotent. More generally, a countable discrete group is strongly amenable if and only if none of its quo...

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Veröffentlicht in:arXiv.org 2019-06
Hauptverfasser: Frisch, Joshua, Tamuz, Omer, Pooya Vahidi Ferdowsi
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Mathematics - Dynamical Systems
Mathematics - Group Theory
Quotients
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description A group is said to be strongly amenable if each of its proximal topological actions has a fixed point. We show that a finitely generated group is strongly amenable if and only if it is virtually nilpotent. More generally, a countable discrete group is strongly amenable if and only if none of its quotients have the infinite conjugacy class property.
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Mathematics - Group Theory
Quotients
title Strong amenability and the infinite conjugacy class property
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