Preprint
Oct 2026
Failure of direct finiteness for group algebras in every odd characteristic
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 $c\ne0$. Thus $\mathbb{F}_p[G_p]$, and the group algebra over every field of characteristic $p$, fails to be directly finite. The construction combines a single exceptional self-...
Elena Bunina, Winston Lee, A. Miasnikov et al.
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