A counterexample to the unit conjecture for group rings

Gardam Giles

Zusammenfassung

The unit conjecture, commonly attributed to Kaplansky, predicts that if K is a field and G is a torsion-free group, then the only units of the group ring K[G] are the trivial units, that is, the non-zero scalar multiples of group elements. We give a concrete counterexample to this conjecture; the group is virtually abelian and the field is order two.