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MR1866850 (2002j:60009) 60B15 (20F10 20M05 60G50) Grigorchuk, Rostislav I.; Żuk, Andrzej The lamplighter group as a group generated by a 2-state automaton, and its spectrum. Geom. Dedicata 87 (2001), no. 1-3, 209--244.

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