On Schur rings over cyclic groups, II

Abstract

In this paper, we show that for any Schur ring S over a cyclic group G, if every subgroup is an S-subgroup, then S is either a wedge product of Schur rings over smaller cyclic groups, or every S-principal subset is an orbit of an element under a fixed subgroup of Aut G. With an earlier result proved by us (on Schur rings over cyclic groups, preprint), we are able to determine all possible structures of Schur rings over a cyclic group. © 1996 Academic Press, Inc.