On Schur groups

I. Ponomarenko

A finite group \(G\) is called Schur, if every Schur ring over \(G\) is the transitivity module of an appropriate permutation group that contains a regular subgroup isomorphic to \(G\). We present recent results on abelian Schur groups that were obtained in a joint work with S.Evdokimov and I.Kovács. We also discuss a new result obtained in a joint work with A.Vasil'ev that any nonabelian Schur group \(G\) is metabelian.