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7. BiLipschitz Embeddings of Groups


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      Problem 7.1.

      [Florent Baudier] Does the planar lamplighter group $\mathbb{Z}_2 \wr \mathbb{Z}^2$ biLipschitzly embed into $L_1$?
        1. Remark. The preprint https://arxiv.org/abs/2608.16706 answers the question in the negative.


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              Problem 7.2.

              [Chris Gartland] Does $\mathrm{SL}_3(\mathbb{Z})$ biLipschitzly embed into $L_1$?

                  Cite this as: AimPL: Metric embeddings, available at http://aimpl.org/metricembeddings.