5 problems

Local indicability conjecture. Every left ordered $\operatorname{NF}$-group is locally indicable.

Let $Y$ be a finite connected $2$-dimensional $CW$-complex. A connected tower with target $Y$ is a finite sequence of covering maps and embeddings … Call such a tower non-positive…

A group $G$ is a Lewin group if, for every field $F$ with a $G$-action, the crossed product $F\ast G$ admits a Hughes-free $F\ast G$-division ring that is its universal division ri…

Let $R$ be a skew field and let $G$ be a locally indicable group. When it exists, let ${\mathcal{D}}_{RG}$ denote the Hughes-free skew field of $RG$. Hughes-free skew-field existen…

Let $K$ be a field and let $G$ be a locally indicable group. A Hughes-free division $K[G]$-ring is an epic division $K[G]$-ring that is $(N,H)$-free for every pair of subgroups…