Vol. 84, No. 2, 1979

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The o-primitive components of a regular ordered permutation group

Maureen A. Bardwell

Vol. 84 (1979), No. 2, 261–274

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.

Mathematical Subject Classification 2000
Primary: 06F15
Secondary: 20B22
Received: 21 August 1978
Published: 1 October 1979
Maureen A. Bardwell