Products of derangements in simple permutation groups

Michael Larsen; Aner Shalev; Pham Huu Tiep

doi:10.1017/fms.2022.69

Products of derangements in simple permutation groups

Michael Larsen, Aner Shalev, Pham Huu Tiep

Einstein Institute of Mathematics

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

Abstract

We prove that any element in a sufficiently large transitive finite simple permutation group is a product of two derangements.

Original language	American English
Article number	e83
Journal	Forum of Mathematics, Sigma
Volume	10
DOIs	https://doi.org/10.1017/fms.2022.69
State	Published - 23 Sep 2022

Bibliographical note

Funding Information:
Michael Larsen was partially supported by the NSF (grants DMS-1702152 and DMS-2001349). Aner Shalev was partially supported by ISF grant 686/17 and the Vinik Chair of mathematics, which he holds. Pham Tiep was partially supported by the NSF (grants DMS-1840702 and DMS-2200850), the Simons Foundation, the Joshua Barlaz Chair in Mathematics and the Charles Simonyi Endowment at the Institute for Advanced Study (Princeton). Part of this work was done while AS and PT participated in the program ‘Groups, Representations and Applications: New Perspectives’ at the Isaac Newton Institute for Mathematical Sciences in 2020. This work was supported by EPSRC grant number EP/R014604/1. All three authors were partially supported by BSF grants 2016072 and 2020037.

Publisher Copyright:
© The Author(s), 2022. Published by Cambridge University Press.

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10.1017/fms.2022.69

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title = "Products of derangements in simple permutation groups",

abstract = "We prove that any element in a sufficiently large transitive finite simple permutation group is a product of two derangements.",

author = "Michael Larsen and Aner Shalev and Tiep, {Pham Huu}",

note = "Funding Information: Michael Larsen was partially supported by the NSF (grants DMS-1702152 and DMS-2001349). Aner Shalev was partially supported by ISF grant 686/17 and the Vinik Chair of mathematics, which he holds. Pham Tiep was partially supported by the NSF (grants DMS-1840702 and DMS-2200850), the Simons Foundation, the Joshua Barlaz Chair in Mathematics and the Charles Simonyi Endowment at the Institute for Advanced Study (Princeton). Part of this work was done while AS and PT participated in the program {\textquoteleft}Groups, Representations and Applications: New Perspectives{\textquoteright} at the Isaac Newton Institute for Mathematical Sciences in 2020. This work was supported by EPSRC grant number EP/R014604/1. All three authors were partially supported by BSF grants 2016072 and 2020037. Publisher Copyright: {\textcopyright} The Author(s), 2022. Published by Cambridge University Press.",

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doi = "10.1017/fms.2022.69",

language = "American English",

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AU - Shalev, Aner

AU - Tiep, Pham Huu

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AB - We prove that any element in a sufficiently large transitive finite simple permutation group is a product of two derangements.

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JO - Forum of Mathematics, Sigma

JF - Forum of Mathematics, Sigma

M1 - e83

ER -

Products of derangements in simple permutation groups

Abstract

Bibliographical note

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