Zero-groups and maximal tori [article]

Alessandro Berarducci
<span title="2005-11-07">2005</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We give a presentation of various results on zero-groups in o-minimal structures together with some new observations. In particular we prove that if G is a definably connected definably compact group in an o-minimal expansion of a real closed field, then for any maximal definably connected abelian subgroup T of G, G is the union of the conjugates of T. This can be seen as a generalization of the classical theorem that a compact connected Lie group is the union of the conjugates of any of its maximal tori.
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="">arXiv:math/0511162v1</a> <a target="_blank" rel="external noopener" href="">fatcat:7o3r6zxshfdsxjb5nc3akrgsiq</a> </span>
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