Groups elementarily equivalent to a free nilpotent group of finite rank (Q639689)

The full classification of finitely generated nilpotent groups up to elementary equivalence is a wide open problem, and in the paper under review the authors address the case of free nilpotent groups of finite rank. They give a complete algebraic description of groups elementarily equivalent to the P. Hall completion of a given free nilpotent group of finite rank over an arbitrary binomial domain. In particular, they characterize all groups elementarily equivalent to a free nilpotent group of finite rank.