The negative answer by counterexample to the *Modular Isomorphism Problem*
for group rings (that is, the question whether for $p$-groups $G$ and $H$,
the group rings ${\mathbb F}_p G$ and ${\mathbb F}_p H$ are isomorphic
only if $G$ and $H$ are isomorphic) by Garcia-Lucas, Margolis and del Rio.

<cite authors="García-Lucas, Diego; Margolis, Leo; del Río, Ángel">_García-Lucas, Diego; Margolis, Leo; del Río, Ángel_, [**Non-isomorphic 2-groups with isomorphic modular group algebras**](https://doi.org/10.1515/crelle-2021-0074), J. Reine Angew. Math. 783, 269-274 (2022). [ZBL1514.20019](https://zbmath.org/?q=an:1514.20019).</cite>