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On Coprimality Graphs for Symmetric Groups

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Abstract

For G a group, X a subset of G and π 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 ≠ y and the order of xy is in π. 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.

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Authors and Affiliations

  1. University of Manchester, Manchester, UK

    John Ballantyne, Nicholas Greer & Peter Rowley

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  1. John Ballantyne
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  2. Nicholas Greer
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  3. Peter Rowley
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Correspondence to John Ballantyne.

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Ballantyne, J., Greer, N. & Rowley, P. On Coprimality Graphs for Symmetric Groups. Graphs and Combinatorics 29, 1595–1622 (2013). https://doi.org/10.1007/s00373-012-1239-y

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  • DOI: https://doi.org/10.1007/s00373-012-1239-y

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