Abstract
We consider primitive subgroups G of the symmetric group Sn, and the sizes of their orbits on subsets X of {1,...,n} as n → ∞. We prove a detailed result from which it follows that if the orbits of all large subsets X (with X ≤ n/2) are large then G = An or Sn. Our proof invokes the classification of finite simple groups. Questions of this type arise in the study of the threshold behavior of monotone boolean functions.
Original language | English |
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Pages (from-to) | 310-318 |
Number of pages | 9 |
Journal | Journal of Algebra |
Volume | 287 |
Issue number | 2 |
DOIs | |
State | Published - 15 May 2005 |
Bibliographical note
Funding Information:✩ Research partially supported by the Bi-National Science Foundation United States–Israel Grant 2000-053, and by the Israel Science Foundation. * Corresponding author. E-mail address: [email protected] (A. Shalev).