It is well-known that the
class of right-ordered groups and the class of regular ordered permutation groups
coincide. In this paper, we exploit this connection to investigate the component parts
of an arbitrary regular o-permutation group. We show that there exist regular
o-permutation groups with nonregular o-primitive components. We show how to
construct a regular o-permutation group which has any given o-primitive
o-permutation group as its largest component. We investigate consequences of this
construction when o-primitive l-permutation groups are used. We also derive
some of the necessary relationships which must exist between the o-primitive
components of a regular o-permutation group, and we derive a collection of
necessary and sufficient conditions for a regular o-permutation group, which
has a finite number of o-primitive components, to have all its components
regular.
