Substitution of open subhypergroups

Abstract

We generalize the join of hypergroups as follows: If $H$ is an open subhypergroup of a hypergroup $K$ and $W$ a compact subhypergroup of a hypergroup $L$ such that $L/W=H$, then there is a natural hypergroup structure on the disjoint union $M:=(K-H)\cup L$. Properties of this hypergroup $M$ are discussed, and its Haar measure and its dual space are determined. As an application we determine the conjugacy class hypergroups $G^{G}$ as well as the dual hypergroups $\hat{G}$ of some compact groups $G$ which are close to the commutative case.