# 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.

## 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 Symmetric Group; Graph; Coprime; Order; Diameter MSC 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations Dr John Ballantyne 09 Nov 2012 20 Oct 2017 14:13 http://eprints.maths.manchester.ac.uk/id/eprint/1909