On potential counterexamples to the problem of zero divisors

E. Rips constructed a serie of groups such that their group rings have zero divisors. These groups are possible counterexamples to Kaplansky problem on zero divisors. The main problem is to find inside this serie a group without torsion. In this paper are studied simplest groups of this serie. It is given their full classification, described their structure and proven that all of them have 2-torsion.