A descending chain condition for groups definable in o-minimal structures
نویسندگان
چکیده
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 of bounded index and G/G equipped with the “logic topology” is a compact Lie group. These results give partial answers to some conjectures of the fourth author. MSC: 03C64, 22E15
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عنوان ژورنال:
- Ann. Pure Appl. Logic
دوره 134 شماره
صفحات -
تاریخ انتشار 2005