A counterexample to the unit conjecture for group rings

• 成果类型: Article
• 署名作者: Gardam, Giles
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2021.194.3.9
• 发表日期: 2021
• 页码: 967-979
• 关键词: farrell-jones conjecture; unique product; torsion-free

摘要

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.