Niblo, Graham A. and Roller, Martin A.
Groups acting on cubes and Kazhdan's property (T).
Proceedings of the American Mathematical Society, 126, (3), .
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We show that a group G contains a subgroup K with e(G,K) > 1 if and only if it admits an action on a connected cube that is transitive on the hyperplanes and has no fixed point. As a corollary we deduce that a countable group Gwith such a subgroup does not satisfy Kazhdan's property (T).
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