On the counterexamples to the unit conjecture for group rings

2021/08/14 by D. S. Passman, Passman, Donald S. · 1 citation
Mathematics · #16S34 #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2108.06570

openalex publication_date 2021/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We offer two comments on the beautiful papers of Giles Gardam and Alan Murray that yield counterexamples to the Kaplansky unit conjecture. First we discuss the determinants of these units in a certain 4× 4 matrix representation of the group ring. Then we explain why there is a doubly infinite family of units in the Murray paper.

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• The one-sided unit count of F₂[P] at radius four, and an integral separation theorem

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