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Association schemes with given stratum dimensions: on a paper of Peter M. Neumann by Anagnostopoulou-Merkouri, Marina; Cameron, Peter J. is a scholarly article available to read on EtoBox.

What is Association schemes with given stratum dimensions: on a paper of Peter M. Neumann about?

In January 1969, Peter M. Neumann wrote a paper entitled "Primitive permutation groups of degree 3p". The main theorem placed restrictions on the parameters of a primitive but not 2-transitive permutation group of degree three times a prime. The paper was never published, and the results have been superseded by stronger theorems depending on the classification of the finite simple groups, for example a classification of primitive groups of odd degree. However, there are further reasons for being interested in this paper. First, it was written at a time when combinatorial techniques were being introduced into the theory of finite permutation groups, and the paper gives a very good summary and application of these techniques. Second, like its predecessor by Helmut Wielandt on primitive groups of degree 2p, it can be re-interpreted as a combinatorial result concerning association schemes whose common eigenspaces have dimensions of a rather limited form. This result uses neither the primality of p nor the existence of a permutation group related to the combinatorial structure. We extract these results and give details of the related combinatorics.

Author

Anagnostopoulou-Merkouri, Marina; Cameron, Peter J.

Published

2022

Language

EN