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Ostrovskii, Mikhail; Randrianantoanina, Beata
Proceedings of the American Mathematical Society, 11/2019, Letnik: 147, Številka: 11Journal Article
We prove that finite lamplighter groups \{\mathbb{Z}_2\wr \mathbb{Z}_n\}_{n\ge 2} with a standard set of generators embed with uniformly bounded distortions into any non-superreflexive Banach space and therefore form a set of test spaces for superreflexivity. Our proof is inspired by the well-known identification of Cayley graphs of infinite lamplighter groups with the horocyclic product of trees. We cover \mathbb{Z}_2\wr \mathbb{Z}_n by three sets with a structure similar to a horocyclic product of trees, which enables us to construct well-controlled embeddings.
