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arXiv · 1605.04829

The degree of commutativity and lamplighter groups

Charles Garnet Cox
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Abstract

The degree of commutativity of a group $G$ measures the probability of choosing two elements in $G$ which commute. There are many results studying this for finite groups. In [AMV17], this was generalised to infinite groups. In this note, we compute the degree of commutativity for wreath products of the form $\mathbb{Z}\wr \mathbb{Z}$ and $F\wr \mathbb{Z}$ where $F$ is any finite group.

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Charles Garnet Cox. 2018-08-27. The degree of commutativity and lamplighter groups. https://arxiv.org/abs/1605.04829

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