## 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 |
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Pages (from-to) | 512-523 |

Number of pages | 12 |

Journal | Journal of Algebra |

Volume | 421 |

DOIs | |

Publication status | Published - 1 Jan 2015 |

## Keywords

- Primitive groups
- Edge-transitive hypergraph