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Most primitive groups are full automorphism groups of edge-transitive hypergraphs
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dc.contributor.author | Babai, László | |
dc.contributor.author | Cameron, Peter Jephson | |
dc.date.accessioned | 2014-10-29T15:31:06Z | |
dc.date.available | 2014-10-29T15:31:06Z | |
dc.date.issued | 2015-01-01 | |
dc.identifier.citation | Babai , L & Cameron , P J 2015 , ' Most primitive groups are full automorphism groups of edge-transitive hypergraphs ' , Journal of Algebra , vol. 421 , pp. 512-523 . https://doi.org/10.1016/j.jalgebra.2014.09.002 | en |
dc.identifier.issn | 0021-8693 | |
dc.identifier.other | PURE: 156410699 | |
dc.identifier.other | PURE UUID: da847bfd-a087-4822-a87b-a44278c42d25 | |
dc.identifier.other | Scopus: 84908577452 | |
dc.identifier.other | ORCID: /0000-0003-3130-9505/work/58055569 | |
dc.identifier.other | WOS: 000345194400026 | |
dc.identifier.uri | https://hdl.handle.net/10023/5580 | |
dc.description.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. | |
dc.format.extent | 12 | |
dc.language.iso | eng | |
dc.relation.ispartof | Journal of Algebra | en |
dc.rights | 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 | en |
dc.subject | Primitive groups | en |
dc.subject | Edge-transitive hypergraph | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject | BDC | en |
dc.subject.lcc | QA | en |
dc.title | Most primitive groups are full automorphism groups of edge-transitive hypergraphs | en |
dc.type | Journal article | en |
dc.description.version | Preprint | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.contributor.institution | University of St Andrews. Statistics | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.identifier.doi | https://doi.org/10.1016/j.jalgebra.2014.09.002 | |
dc.description.status | Peer reviewed | en |
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