On the Mal′cev correspondence

Abstract:

We generalize Mal’cev’s correspondence [5] to other nilpotent groups, namely to certain maximal unipotent subgroups of Chevalley groups. If $\mathcal {L}$ is a root system and $K$ is an infinite field of characteristic different to 2 or 3, then we show that a group $G$ elementarily equivalent to ${U_\mathcal {L}}(K)$ is isomorphic to ${U_\mathcal {L}}(F)$, where $F$ is a field elementarily equivalent to $K$.