On some elementary properties of soluble groups of derived length 2

Conditions are found for a soluble group of derived length 2 with few relations to be universally equivalent to a free soluble group of derived length 2. The Fitting radical of a soluble group of derived length 2 with few relations coincides with the derived subgroup. Also, if an $n$-generator soluble group is elementarily equivalent to a free soluble group of rank $m$ and derived length $k$ then for $k=2$ or $k>2$ and $n=m$ the groups are isomorphic.