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

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Tartalom: http://dx.doi.org/10.1016/j.jalgebra.2014.09.002
Archívum: MTA Könyvtár
Gyűjtemény: Status = Published

Type = Article
Cím:
Most primitive groups are full automorphism groups of edge-transitive hypergraphs
Létrehozó:
Babai, László
Cameron, P. J.
Dátum:
2015
Téma:
QA72 Algebra / algebra
Tartalmi leírás:
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+? for the minimum size of the edges in such a hypergraph. This is essentially best possible.
Típus:
Article
PeerReviewed
Formátum:
text
Azonosító:
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
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