4 problems

Let $G$ be a torsion-free group, let $\mathbb{F}$ be a field, and let $\mathbb{F}[G]$ be the group ring. The obvious units in $\mathbb{F}[G]$ are the elements $\lambda g$ with…

Let $H$ be a torsion-free group, and let $\mathbb{Z}H$ denote its integral group ring. Write $\pm H$ for the subgroup generated by $H$ and the two-element group generated by $-1$.…

Let $G$) be a torsion-free group and let $K$ be a field. A unit of the group ring $K[G]$ is an element with a multiplicative inverse, and the trivial units are the elements $kg$ wi…

Let $K$ be a field and let $G$ be a torsion-free group. A unit in the group algebra $KG$ means a two-sided multiplicative unit. Unit conjecture. Every unit of $KG$ is trivial, name…