Most primitive groups are full automorphism groups of edge-transitive hypergraphs
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We prove that, for a primitive permutation group G acting on a set of size n, other than the alternating group, the probability that Aut(X,YG) = G for a random subset Y of X, tends to 1 as n tends to infinity. So the property of the title holds for all primitive groups except the alternating groups and finitely many others. This answers a question of M. Klin. Moreover, we give an upper bound n1/2+ε for the minimum size of the edges in such a hypergraph. This is essentially best possible.
Babai , L & Cameron , P J 2015 , ' Most primitive groups are full automorphism groups of edge-transitive hypergraphs ' Journal of Algebra , vol 421 , no. 1 , pp. 512-523 . DOI: 10.1016/j.jalgebra.2014.09.002
Journal of Algebra
Non peer reviewed
© 2014. Elsevier Inc. All rights reserved. This is the preprint version before acceptance of the following article: Most primitive groups are full automorphism groups of edge-transitive hypergraphs, Babai, L. & Cameron, P. J. 1 Jan 2015 In : Journal of Algebra. 421, 1, p. 512-523, which has been published in final form at http://www.sciencedirect.com/science/article/pii/S002186931400489X
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