In this paper we prove the following theorem: Any one-dimensional definably connected group G over an o-minimal structure is, as an abstract group, isomorphic to either ⊕p∈PZp∞⊕⊕δ Q or ⊕δ Q

Let G be a group definable in an o-minimal structure M. In this paper we show: Theorem. If G is a two-dimensional definably connected nonabelian group, then G is centerless and G is isomorphic to R+⋊R∗>0, for some real closed field R. Theorem. If G is a three-dimensional nonsolvable, centerless, definably connected group, then either G ≅ SO3(R) or G ≅ PSL2(R), for some real closed field R.