On cyclic tournaments (Q1196291)

A tournament is an orientation of a complete graph. A tournament \(T\) is called cyclic if its automorphism group \(G(T)\) contains the permutation \(C=(1,2,\dots,n)\), where \(n\) is the number of vertices of \(T\). Let \(W(n)\) denote the set of all subgroups of the symmetric group \(S(n)\) of odd orders containing \(C\). This paper gives a number of results on the structure of \(W(n)\). It is shown that every element of \(W(n)\) is the automorphism group of some cyclic tournament \(T\).