Asymptotic behavior of finite permutation groups acting on subsets

Carmit Benbenisty, Aner Shalev*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 languageAmerican English
Pages (from-to)310-318
Number of pages9
JournalJournal of Algebra
Volume287
Issue number2
DOIs
StatePublished - 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).

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