## 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

## 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 |
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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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