On the isomorphism problem for integral group rings of finite groups (Q1325228)

We give a positive answer to the isomorphism problem for a class of groups \(G\) containing those with abelian normal subgroup \(N\) and nilpotent \(G/N\). The proof depends on a result of the first author in collaboration with L. L. Scott that guarantees that group bases of \(p\)- adic group rings of \(p\)-solvable groups \(G_ p\) without normal subgroup of order relatively prime to \(p\) are conjugate. Our result also covers groups being certain abelian extensions of direct products of groups \(G_ p\) satisfying some additional constraints.