On superstable groups with residual properties

Mathematical Logic Quarterly 53 (1):19-26 (2007)
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Abstract

Given a pseudovariety [MATHEMATICAL SCRIPT CAPITAL C], it is proved that a residually-[MATHEMATICAL SCRIPT CAPITAL C] superstable group G has a finite seriesG0 ⊴ G1 ⊴ · · · ⊴ Gn = Gsuch that G0 is solvable and each factor Gi +1/Gi is in [MATHEMATICAL SCRIPT CAPITAL C] . In particular, a residually finite superstable group is solvable-by-finite, and if it is ω -stable, then it is nilpotent-by-finite. Given a finitely generated group G, we show that if G is ω -stable and satisfies some residual properties , then G is finite

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10.1002/malq.200610023

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Citations of this work

Propriétés résiduelLes dans Les groupes supersimpLes.Frank Wagner - 2011 - Journal of Symbolic Logic 76 (2):361 - 367.

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Superstable groups.Ch Berline & D. Lascar - 1986 - Annals of Pure and Applied Logic 30 (1):1-43.

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