# Applications of the Roggenkamp-Scott theorem ?

In 1987 Roggenkamp and Scott published a solution of the integral isomorphism problem for $p$-groups, i.e. if $G,H$ are $p$-groups and $\mathbb{Z}[G] \cong \mathbb{Z}[H]$ as rings then $G \cong H$.

However, in practice I guess it is at least as hard to show that two group rings aren't isomorphic than to show that the groups itself aren't isomorphic. Therefore I wonder if this theorem (or one of its variants or generalizations) have found applications in group theory. Any idea ?

-

The Annals paper by Roggenkamp and Scott was certainly a landmark in the ongoing study of the isomorphism problem for integral group rings of finite groups, which apparently goes back to the thesis work of Graham Higman and later related work by Richard Brauer. Zassenhaus refined and extended the underlying problem of whether two finite groups with isomorphic group rings over $\mathbb{Z}$ must necessarily be isomorphic.