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2010.64: On Coprimality Graphs for Symmetric Groups

2010.64: John J Ballantyne, Nicholas M Greer and Peter J Rowley (2012) On Coprimality Graphs for Symmetric Groups. Graphs and Combinatorics.

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DOI: 10.1007/s00373-012-1239-y


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 2000 > 20 Group theory and generalizations
MIMS number:2010.64
Deposited By:Dr John Ballantyne
Deposited On:09 November 2012

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