On the automorphism group of the m-coloured random graph
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چکیده
Let Rm be the (unique) universal homogeneous m-edge-coloured countable complete graph (m ≥ 2), and Gm its group of colourpreserving automorphisms. The group Gm was shown to be simple by John Truss. We examine the automorphism group of Gm, and show that it is the group of permutations of Rm which induce permutations on the colours, and hence an extension of Gm 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 Gm in its automorphism group.
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تاریخ انتشار 2007