We follow the proof by Giles Gardam in "A counterexample to the unit conjecture for group rings" (https://arxiv.org/abs/2102.11818) and provide an independent verification of the calculations in GAP.
Click on "launch binder" button to start a Jupyter notebook in which you will be able to follow the steps of the calculation.
Alternatively, you can see the same Jupyter notebook rendered on GitHub at https://github.com/olexandr-konovalov/Kaplansky-units-counterexample/blob/main/counterexample.ipynb.
This repository uses the template for publishing reproducible GAP experiments in Jupyter notebooks runnable on Binder, available at https://github.com/rse-standrewscs/gap-binder-template.