Schurity of the wedge product of association schemes and generalized wreath product of permutation groups

Abstract

The generalized wreath product of permutation groups was introduced by Evdokimov and Ponomarenko in order to study the schurity problem for S-rings over cyclic groups. In this paper we construct the generalized wreath product of permutation groups by a method entirely different from Evdokimov and Ponomarenko's construction. Then we give a necessary and sufficient condition for the wedge product of schurian association schemes coming from the generalized wreath product of permutation groups. © 2020 Elsevier B.V.