Most primitive groups are full automorphism groups of edge-transitive hypergraphs

László Babai; Peter Jephson Cameron

doi:10.1016/j.jalgebra.2014.09.002

Most primitive groups are full automorphism groups of edge-transitive hypergraphs

László Babai, Peter Jephson Cameron

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Abstract

We prove that, for a primitive permutation group G acting on a set X of size n, other than the alternating group, the probability that Aut (X,Y^G) = G for a random subset Y of X, tends to 1 as n → ∞. 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.H. Klin. Moreover, we give an upper bound n^1/2+ε for the minimum size of the edges in such a hypergraph. This is essentially best possible.

Original language	English
Pages (from-to)	512-523
Number of pages	12
Journal	Journal of Algebra
Volume	421
DOIs	https://doi.org/10.1016/j.jalgebra.2014.09.002
Publication status	Published - 1 Jan 2015

Keywords

Primitive groups
Edge-transitive hypergraph

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10.1016/j.jalgebra.2014.09.002

babai-cameron5
Copyright © 2014. the Author(s). 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
Submitted manuscript, 275 KB

Peter Jephson Cameron
- pjc20st-andrews.acuk
- Pure Mathematics - Professor
- Centre for Interdisciplinary Research in Computational Algebra
Person: Academic

Cite this

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Most primitive groups are full automorphism groups of edge-transitive hypergraphs

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Peter Jephson Cameron

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