Generalized dihedral CI-groups

In this paper, we find a strong new restriction on the structure of CI-groups. We show that, if R is a generalised dihedral group and if R is a CI-group, then for every odd prime p the Sylow p -subgroup of R has order p , or 9 . Consequently, any CI-group with quotient a generalised dihedral group has the same restriction, that for every odd prime p the Sylow p -subgroup of the group has order p , or 9 .