On coprimality graphs for symmetric groups

John Ballantyne; Nicholas Greer; Peter Rowley

doi:10.1007/s00373-012-1239-y

On coprimality graphs for symmetric groups

John Ballantyne, Nicholas Greer, Peter Rowley

Department of Mathematics

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

Abstract

For G a group, X a subset of G and π a set of positive integers we define
a graph Cπ (G, X) whose vertex set is X with x, y ∈ X joined by an edge provided
x = y and the order of xy is in π. Here we investigate Cπ (G, X) when G is a finite
symmetric group and X is a G-conjugacy class of elements of order p, p a prime.

Original language	English
Pages (from-to)	1595-1622
Number of pages	28
Journal	Graphs and Combinatorics
Volume	29
Issue number	6
DOIs	https://doi.org/10.1007/s00373-012-1239-y
Publication status	Published - 31 Oct 2012

Keywords

Symmetric group
Graph
Coprime
Order
Diameter

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10.1007/s00373-012-1239-y

https://doi-org.manchester.idm.oclc.org/10.1007/s00373-012-1239-y

Cite this

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title = "On coprimality graphs for symmetric groups",

abstract = "For G a group, X a subset of G and π a set of positive integers we definea graph Cπ (G, X) whose vertex set is X with x, y ∈ X joined by an edge providedx = y and the order of xy is in π. Here we investigate Cπ (G, X) when G is a finitesymmetric group and X is a G-conjugacy class of elements of order p, p a prime.",

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AU - Greer, Nicholas

AU - Rowley, Peter

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KW - Symmetric group

KW - Graph

KW - Coprime

KW - Order

KW - Diameter

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DO - 10.1007/s00373-012-1239-y

M3 - Article

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JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

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ER -

On coprimality graphs for symmetric groups

Abstract

Keywords

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