Permutations with orders coprime to a given integer

John Bamberg; S. P. Glasby; Scott Harper; Cheryl E. Praeger

doi:10.37236/8678

Permutations with orders coprime to a given integer

John Bamberg, S. P. Glasby, Scott Harper, Cheryl E. Praeger

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

4 Citations (Scopus)

Abstract

Let m be a positive integer and let ρ (m; n) be the proportion of permutations of the symmetric group Sym(n) whose order is coprime to m. In 2002, Pouyanne proved that (Formula Presented) where K_m is a complicated (unbounded) function of m. We show that there exists a positive constant C(m) such that, for all n > m, (Formula Presented) where ϕ is Euler's totient function.

Original language	English
Article number	P1.6
Number of pages	14
Journal	Electronic Journal of Combinatorics
Volume	27
Issue number	1
DOIs	https://doi.org/10.37236/8678
Publication status	Published - 2020

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10.37236/8678Licence: CC BY-NC-ND

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title = "Permutations with orders coprime to a given integer",

abstract = "Let m be a positive integer and let ρ (m; n) be the proportion of permutations of the symmetric group Sym(n) whose order is coprime to m. In 2002, Pouyanne proved that (Formula Presented) where Km is a complicated (unbounded) function of m. We show that there exists a positive constant C(m) such that, for all n > m, (Formula Presented) where ϕ is Euler's totient function.",

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AU - Harper, Scott

AU - Praeger, Cheryl E.

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N2 - Let m be a positive integer and let ρ (m; n) be the proportion of permutations of the symmetric group Sym(n) whose order is coprime to m. In 2002, Pouyanne proved that (Formula Presented) where Km is a complicated (unbounded) function of m. We show that there exists a positive constant C(m) such that, for all n > m, (Formula Presented) where ϕ is Euler's totient function.

AB - Let m be a positive integer and let ρ (m; n) be the proportion of permutations of the symmetric group Sym(n) whose order is coprime to m. In 2002, Pouyanne proved that (Formula Presented) where Km is a complicated (unbounded) function of m. We show that there exists a positive constant C(m) such that, for all n > m, (Formula Presented) where ϕ is Euler's totient function.

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UR - https://arxiv.org/abs/1807.10450

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ER -

Permutations with orders coprime to a given integer

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Complexity of group algorithms and statistical fingerprints of groups

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Permutations with orders coprime to a given integer

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Complexity of group algorithms and statistical fingerprints of groups

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