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arXiv · 2610.10417

On the residual finiteness of the non-abelian exterior square of wreath products and the Grigorchuk group

Ayrton Anjos Teixeira·Dessislava H. Kochloukova
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Abstract

We show some sufficient conditions ( in terms of properties of $A$, $B$ and $X$) for the non-abelian exterior square $G \wedge G$ to be residually finite, where $G $ is the wreath product $A \wr B$ or the combinatorial wreath product $G = A \wr_X B$, in the latter case $B$ is a free group. We prove that for the Grigorchuk group $G$ the non-abelian exterior square $G \wedge G$ and the non-abelian tensor product $G \otimes G$ are residually finite. We show conditions that imply that $A \wr B$ is not (cohomologically) good in dimension $\leq 2$.

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Ayrton Anjos Teixeira, Dessislava H. Kochloukova. 2026-10-07. On the residual finiteness of the non-abelian exterior square of wreath products and the Grigorchuk group. https://arxiv.org/abs/2610.10417

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