Failure of direct finiteness for group algebras in every odd characteristic

Elena I. Bunina, Winston Lee, Alexei Miasnikov +1

For every odd prime $p$, we construct a finitely presented group $G_p$ and elements $a,b,c\in {\mathbb{F}}_p[G_p]$ such that $ab=1$, $ac=0$, and $c\ne 0$. Thus ${\mathbb{F}}_p[G_p]$, and…