On the automorphism group of the m-coloured random graph

Peter J. Cameron; Sam Tarzi

paper

On the automorphism group of the m-coloured random graph

arXiv:1708.07831

Abstract

Let $R_{m}$ be the (unique) universal homogeneous $m$ -edge-coloured countable complete graph ( $m \geq 2$ ), and $G_{m}$ its group of colour-preserving automorphisms. The group $G_{m}$ was shown to be simple by John Truss. We examine the automorphism group of $G_{m}$ , and show that it is the group of permutations of $R_{m}$ which induce permutations on the colours, and hence an extension of $G_{m}$ by the symmetric group of degree $m$ . We show further that the extension splits if and only if $m$ is odd, and in the case where $m$ is even and not divisible by~ $8$ we find the smallest supplement for $G_{m}$ in its automorphism group. (This unpublished paper from 2007 is placed here because of renewed interest in the topic.)

arXiv commentPaper from 2007 placed here because of renewed interest in the topic. arXiv admin note: substantial text overlap with arXiv:1406.7870

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