The Group of Recursive Amorphisms of the Universal Random Graph
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The random graph is an interesting mathematical structure which was discovered by Renyi and Erdos in 1963. The group of the automorphisms of the random graph was studied in depth by Truss in 1985 and turns out to be what is known as an oligomorphic permutation group, and as such was studied by Peter Cameron in 1990. In that work, he raised the question: what is the structure of the recursive automorphisms of a recursive model of the random graph. This paper partially answers this question by showing that the group in question is countable, primitive and simple, as well as explores some of the group's topological properties. The group of primitive recursive automorphisms is studied as well.