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.