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We prove that a wreath product of an abelian group and a non-amenable groupis not strongly Ulam stable. Previously this was known for groups containingfree subgroups, due to work of Burger, Ozawa and Thom, and for some surfacegroups, due to work by Kazhdan. We also show that these wreath products are notdeformation rigid.

Lamplighters over non-amenable groups are not strongly Ulam stable