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Combinatorial Mathematics IX: Proceedings of the Ninth by D. R. Breach (auth.), Elizabeth J. Billington, Sheila

By D. R. Breach (auth.), Elizabeth J. Billington, Sheila Oates-Williams, Anne Penfold Street (eds.)

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Extra info for Combinatorial Mathematics IX: Proceedings of the Ninth Australian Conference on Combinatorial Mathematics Held at the University of Queensland, Brisbane, Australia, August 24–28, 1981

Example text

Case I is 2- Then any such group is 3-homogeneous. (c) is done as before. also fails, since P r o p o s i t i o n to consider cases m i n i m a l blocks, ever, is similar. (a) and This time, the proof in case (b) together. and define the r e l a t i o n Choose, as before, a system of x I yz Now, how- as before. the r e l a t i o n may not hold at all w i t h i n a triple good if it does hold. 3 does not apply, and it is convenient {x,y,z}. It is easily seen that G We is transitive on good triples.

On each orbit, By since it is bounded there is a point of L to the order). It follows is 2-transitive but not 2-primitive. which is easily that G is (s+l)-homogeneous. Case called (b): G 2-primitive is primitive if it is transitive 3-transitive. 4, relation or a circular order. (c): hence Step 2. G G Then certainly preserves and so primitive. resembling is 2-primitive. S-homogeneous; so case The case division, either a betweenness that G x is primitive is (s+l)-homogeneous. ) whence and for any triple z Subcase c = i.

Amer. Math. 850-854. M~biusebenen Gerader Ordnung, Math. Ann. 157 (1964) 179-205. [6] P. F. Denniston, (1976) [7] (Springer-Verlag, Geometries Berlin-Heidelberg- 1968). Some new S-designs, Bull. Lond. Math. Amer. J. Math. Soc. 8 263-267. R. Hughes, On t-designs and groups, 87 (1965) 761-778. R. C. M. Kantor, Dimenslon lattices, [i0] H. L~neberg, York, [ii] V. Pless, Lecture Notes Berlin-Heidelberg-New J. Combin. 12 (1972) 119-142. 12 (1938) 265-275. Department of Mathematics University of Canterbury Gruppen van Mathieu, Abh.

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