2012.7: Local Fusion Graphs for Symmetric Groups

2012.7: John J Ballantyne, Nicholas M Greer and Peter J Rowley (2012) Local Fusion Graphs for Symmetric Groups. Journal of Group Theory.

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DOI: 10.1515/jgt-2012-0027

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 $\pi$.

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