Asymptotic behavior of finite permutation groups acting on subsets

Carmit Benbenisty; Aner Shalev

doi:10.1016/j.jalgebra.2005.02.008

Asymptotic behavior of finite permutation groups acting on subsets

Carmit Benbenisty
, Aner Shalev^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider primitive subgroups G of the symmetric group S_n, 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 = A_n or S_n. 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
Pages (from-to)	310-318
Number of pages	9
Journal	Journal of Algebra
Volume	287
Issue number	2
DOIs	https://doi.org/10.1016/j.jalgebra.2005.02.008
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).

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10.1016/j.jalgebra.2005.02.008

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N2 - 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.

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Asymptotic behavior of finite permutation groups acting on subsets

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Bibliographical note

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