On Potential Counterexamples to the Problem of Zero Divisors

Resumo

E. Rips constructed a series of groups such that their group rings have zero divisors. such groups can serve as counterexamples to Kaplansky’s problem on zero divisors. The problem is to find such a group without torsion. We study simplest groups of this series, classify such groups, describe the structure, and show that all such groups have 2-torsion.