Hypergroups Related to a Pair of Compact Hypergroups

The purpose of the present paper is to investigate a hypergroup associated with irreducible characters of a compact hypergroup $H$ and a closed subhypergroup $H_0$ of $H$ with $\mathrm{\mid }H\mathrm{/}{H}_0\mathrm{\mid }<+\mathrm{\infty }$. The convolution of this hypergroup is introduced by inducing irreducible characters of $H_0$ to $H$ and by restricting irreducible characters of $H$ to $H_0$. The method of proof relies on the notion of an induced character and an admissible hypergroup pair.