Rigidity of amalgamated free products in measure equivalence

摘要

A discrete countable group r is said to be ME rigid if any discrete countable group that is ME to F is virtually isomorphic to F. 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.