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arXiv · 2102.11818

A counterexample to the unit conjecture for group rings

Giles Gardam
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Abstract

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.

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Giles Gardam. 2021-02-23. A counterexample to the unit conjecture for group rings. https://doi.org/10.4007/annals.2021.194.3.9

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