A combinatorial approach to transitive extensions of generously unitransitive permutation groups
by
Mikhail Klin
Ben-Gurion University of the Negev
Coauthors: Dale Mesner, Andrew Woldar

We suggest a combinatorial approach to the construction of transitive extensions of generously unitranstive permutation groups. Three types of combinatorial structures are considered, namely compatible families of triple designs, coherent families of triple designs and symmetric association schemes on triples. Necessary conditions for the existence of transitive extension are formulated in terms of the suggested structures. A number of examples are considered as well as application of the developed techniques to the extensions of classical Hamming association schemes.

Date received: May 14, 2008