零群与极大环面
Zero-groups and maximal tori
摘要：
我们给出了各种结果的零群的o-极小结构连同一些新的观察。特别地，我们证明了：如果G是实封闭的域的o-极小扩张中的可定义连通可定义紧群，则对G的任意极大可定义连通交换子群T，G是T的共轭的并.这可以看作是经典定理的推广，即紧连通李群是它的任何极大环面的共轭的并集。
英文摘要：
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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