On Coprimality Graphs for Symmetric Groups

Ballantyne, John J and Greer, Nicholas M and Rowley, Peter J (2012) On Coprimality Graphs for Symmetric Groups. Graphs and Combinatorics.

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Abstract

For a group $G$, $X$ a subset of $G$ and $\pi$ a set of positive integers we define a graph $\mathcal{C}_\pi(G,X)$ whose vertex set is $X$ with $x, y \in X$ joined by an edge provided $x \neq y$ and the order of $xy$ is in $\pi$. Here we investigate $\mathcal{C}_\pi(G,X)$ when $G$ is a finite symmetric group and $X$ is a $G$-conjugacy class of elements of order $p$, $p$ a prime.

Item Type:	Article
Uncontrolled Keywords:	Symmetric Group; Graph; Coprime; Order; Diameter
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations
Depositing User:	Dr John Ballantyne
Date Deposited:	09 Nov 2012
Last Modified:	20 Oct 2017 14:13
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/1909

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