We study definably compact definably connected groups definable in a sufficiently saturated real closed field R . Our main result is that for such a kind of groups G that are also abelian, there is a Zariski-connected R -algebraic group H such that the o-minimal universal covering group of G is, up to a locally definable isomorphism, an open connected locally definable subgroup $$\mathcal{W}$$ W of the o-minimal universal covering group of H ( R ) 0 . Thus, G is definably isomorphic to the definable quotient of $$\mathcal{W}$$ W by a discrete subgroup.

中文翻译：

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可在真实封闭域中定义的可定义紧群

我们研究了在足够饱和的实闭域 R 中可定义的可定义紧可定义连接群。我们的主要结果是，对于这种同样是阿贝尔群的群 G，存在一个 Zariski 连通的 R-代数群 H，使得 G 的 o-最小通用覆盖群是，直到局部可定义的同构，一个开H ( R ) 0 的 o 极小泛覆盖群的连通局部可定义子群 $$\mathcal{W}$$ W 。因此，通过离散子群，G 与 $$\mathcal{W}$$ W 的可定义商是可定义的同构。