2014/04/30 by László Babai, Laszlo Babai, Peter J. Cameron +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Alternating group #Automorphism #Automorphism group #Combinatorics #Computer science #Cooperative Communication and Network Coding #Discrete mathematics #Enhanced Data Rates for GSM Evolution #Finite Group Theory Research #Genomic variations and chromosomal abnormalities #Group (periodic table) #Hypergraph #Mathematics #Permutation (music) #Permutation group #Physics #Set (abstract data type) #Transitive relation #Upper and lower bounds #math.GR #msc:05C65 #msc:20B15
paper · pdf · doi:10.1016/j.jalgebra.2014.09.002
To appear in special issue of Journal of Algebra in memory of Akos Seress
arxiv created 2014/09/08 · arxiv updated 2014/09/09 · openalex publication_date 2014/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We prove that, for a primitive permutation group G acting on a set 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 tends to infinity. 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. 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.