Local Fusion Graphs for Symmetric Groups

Ballantyne, John J and Greer, Nicholas M and Rowley, Peter J (2012) Local Fusion Graphs for Symmetric Groups. Journal of Group Theory. (In Press)

Abstract

For a group $G$, $\pi$ a set of odd positive integers and $X$ a set of involutions of $G$ we define a graph $\mathcal{F}_\pi(G,X)$. This graph, called a $\pi$-local fusion graph, has vertex set $X$ with $x,y \in X$ joined by an edge provided $x \neq y$ and the order of $xy$ is in $\pi$. In this paper we investigate $\mathcal{F}_\pi(G,X)$ when $G$ is a finite symmetric group for various choices of $X$ and $\pi$.

Item Type: Article symmetric group, involution, graph 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/1910