6 problems

Let $\mathbb{K}$ be a subfield of $\mathbb{C}$, and let $G$ be a countable group with a bound on the orders of its finite subgroups. For a finite matrix $A$ over $\mathbb{K}[G]$, l…

Let $G$ be a torsion-free group and let $kG$ be its group algebra over a field $k$. A division ring has the Linnell property when it has the property referred to in the source. Jai…

Let $G$ be a group in the class $\mathcal{T}$ with finite $\operatorname{lcm}(G)$, and let $K\subseteq\mathbb{C}$ be any subfield closed under complex conjugation. Let…

Let $G$ be a countable group with finite $\operatorname{lcm}(G)$, and let $K\subseteq\mathbb{C}$ be a field closed under complex conjugation. Let $\mathcal{N}(G)$ be the group von…

Let $G$ be a countable group with finite $\operatorname{lcm}(G)$, and let $K\subseteq\mathbb{C}$ be a field closed under complex conjugation. For each finite subgroup…

Analytic zero-divisor conjecture. If $0 \neq \alpha \in \mathbb{C}G$ and $0 \neq f \in \ell^2(G)$, then