Annalisa Conversano

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In the last twenty years many authors have investigated the analogies between groups definable in o-minimal structures and real Lie groups (see [Ot] for a survey). By a theorem of Pillay ([Pi1]), every definable group G in an o-minimal structure M can be equipped with a topology τ which makes it a topological group. Moreover, if n ∈ N is the o-minimal(More)
We prove the definability, and actually the finiteness of the commu-tator width, of many commutator subgroups in groups definable in o-minimal structures. It applies in particular to derived series and to lower central series of solvable groups. Along the way, we prove some generalities on groups with the descending chain condition on definable subgroups(More)
We study analogues of the notions from Lie theory of Levi subgroup and Levi decomposition, in the case of groups G definable in an o-minimal expansion of a real closed field. With suitable definitions, we prove that G has a unique maximal ind-definable semisimple subgroup S, up to conjugacy, and that G = R · S where R is the solvable radical of G. We also(More)
In this sequel to [3] we try to give a comprehensive account of the " connected components " G 00 and G 000 as well as the various quotients G/G 00 , G/G 000 , G 00 /G 000 , for G a group definable in a (saturated) o-minimal expansion of a real closed field. Key themes are the structure of G 00 /G 000 and the problem of " exactness " of the G → G 00(More)
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