Serial group rings of finite groups. \(p\)-solvability

Abstract

We prove that for any finite \(p\)-solvable group \(G\) with a cyclic \(p\)-Sylow subgroup and any field \(F\) of characteristic \(p\), the group ring \(FG\) is serial. As a corollary for an arbitrary field we will produce a list of all groups of order \(\leq 100\) whose group rings are serial.