Babai, László and Cameron, P. J.
(2015)
*Most primitive groups are full automorphism groups of edge-transitive hypergraphs.*
Journal of Algebra, 421.
pp. 512-523.
ISSN 0021-8693

Text
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Official URL: http://dx.doi.org/10.1016/j.jalgebra.2014.09.002

## 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, YG)=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 n1/2+ε for the minimum size of the edges in such a hypergraph. This is essentially best possible.

Item Type: | Article |
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Uncontrolled Keywords: | Primitive group; Edge-transitive hypergraph |

Subjects: | Q Science / természettudomány > QA Mathematics / matematika > QA72 Algebra / algebra |

SWORD Depositor: | MTMT SWORD |

Depositing User: | MTMT SWORD |

Date Deposited: | 16 Feb 2016 14:58 |

Last Modified: | 16 Feb 2016 14:58 |

URI: | http://real.mtak.hu/id/eprint/33569 |

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