Members & Former Members

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.

Related project(s):
48Profinite and RFRS groups