Geodesic
The Group of the Quadratic Residue Tournament
Canadian mathematical bulletin, Tome 13 (1970) no. 1, pp. 51-54

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A tournament Tn is a set of n nodes a 1a 2, ..., an such that every pair (ai , aj ) of distinct nodes is joined by exactly one of the oriented edges or . If is in Tn , then we say that ai dominates aj and write ai → aj .The (automorphism) group G(Tn ) of a tournament Tn is the group of all permutations φ of the nodes of Tn such that φ(a)→φ(b) if and only if a → b. It is known [9] that there exist tournaments whose group is abstractly isomorphic to a given group H if and only if H has odd order; thus all tournament groups are solvable, by the Feit-Thompson Theorem [7]. 
Goldberg, Myron. The Group of the Quadratic Residue Tournament. Canadian mathematical bulletin, Tome 13 (1970) no. 1, pp. 51-54. doi: 10.4153/CMB-1970-010-8
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