Prof. Dr. Giles Gardam
Project leader
Universität Bonn
E-mail: gardam(at)math.uni-bonn.de
Homepage: https://www.gilesgardam.com/ _blank
Project
48Profinite and RFRS groups
Publications within SPP2026
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