Open Research Index

A group without fixed price

OpenAI

OpenAI Mathopenai-math/A-group-without-fixed-priceOct 5, 2026math.GRAI-generatedscore 0

We construct a finitely generated group with two essentially free probability-measure-preserving actions of different costs. This gives a negative answer to Gaboriau's general fixed-price problem. The group is an amalgam of a free group of rank 100 with a direct product. Its Bernoulli action has cost bounded away from one, whereas finite height extensions have costs tending to one.

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