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arXiv · 1801.04024

Strong amenability and the infinite conjugacy class property

Joshua Frisch·Omer Tamuz·Pooya Vahidi Ferdowsi
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Abstract

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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Joshua Frisch, Omer Tamuz, Pooya Vahidi Ferdowsi. 2019-06-06. Strong amenability and the infinite conjugacy class property. https://doi.org/10.1007/s00222-019-00896-z

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