We prove that if G is a group definable in a saturated o-minimal structure, then G has no infinite descending chain of type-definable subgroups of bounded index. Equivalently, G has a smallest (necessarily normal) type-definable subgroup G 00 of bounded index and G/G 00 equipped with the “logic topology” is a compact Lie group. These results give partial answers to some conjectures of the fourth author.

A descending chain condition for groups definable in o-minimal structures

BERARDUCCI, ALESSANDRO;
2005-01-01

Abstract

We prove that if G is a group definable in a saturated o-minimal structure, then G has no infinite descending chain of type-definable subgroups of bounded index. Equivalently, G has a smallest (necessarily normal) type-definable subgroup G 00 of bounded index and G/G 00 equipped with the “logic topology” is a compact Lie group. These results give partial answers to some conjectures of the fourth author.
2005
Berarducci, Alessandro; M., Otero; Y., Peterzil; A., Pillay
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/94954
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