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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.