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External Paradoxical Decompositions
Authors:John Donnelly
Institution:(1) Department of Mathematics, Mount Union College, 1972 Clark Avenue, Alliance, OH 44601, USA
Abstract:Ore's condition states that a cancellative semigroup S which has common right multiples embeds into a group G such that certain properties are satisfied by S and G. We show that G is nonamenable if and only if the semigroup S-1 is G-paradoxical with respect to right multiplication by elements of S. We explore certain properties of this decomposition of S-1.
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