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On superstable groups with residual properties

✍ Scribed by Abderezak Ould Houcine

Publisher: John Wiley and Sons
Year: 2007
Tongue: English
Weight: 156 KB
Volume: 53
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200610023

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✦ Synopsis

Given a pseudovariety C, it is proved that a residually-C superstable group G has a finite series

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 (residual solvability, residual finiteness, . . . ), then G is finite.

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