Zero-groups and maximal tori

Details Zero-groups and maximal tori Zero-groups and maximal tori

2005-11-07

arxiv.org/abs/math/0511162v1

Mathematics

Logic

Scientific paper

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.

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