Serial group rings of finite groups. p-solvability - Kukharev, A.; Puninski, G. (Algebra and Discrete Mathematics, 2013)
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 ≤ 100 whose group rings are serial.