Rigidity of amalgamated free products in measure equivalence
Abstract
A discrete countable group is said to be ME rigid if any discrete countable group that is measure equivalent to is virtually isomorphic to . In this paper, we construct ME rigid groups by amalgamating two groups satisfying rigidity in a sense of measure equivalence. A class of amalgamated free products is introduced, and discrete countable groups which are measure equivalent to a group in that class are investigated.
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