More Counterexamples to the Unit Conjecture for Group Rings

TL;DR

This paper extends previous work by providing a family of counterexamples to Kaplansky's unit conjecture in group rings for all prime characteristics, challenging a long-standing assumption in algebra.

Contribution

It introduces a new family of counterexamples to the unit conjecture applicable across all prime characteristics, broadening the scope of known exceptions.

Findings

Counterexamples exist for every prime characteristic.

The family of counterexamples generalizes previous specific cases.

The results challenge the universality of Kaplansky's unit conjecture.

Abstract

Extending the discovery by Giles Gardam of a concrete counterexample to Kaplansky's unit conjecture in characteristic 2, a family of counterexamples for every prime characteristic is presented.