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

Alessandro Berarducci, Margarita Otero, Yaa'cov Peterzil, Anand Pillay
2005 Annals of Pure and Applied Logic  
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.
doi:10.1016/j.apal.2005.01.002 fatcat:pmfn2atkljazpfzkl2ly3sg6fq