Automorphisms and enumeration of switching classes of tournaments (Q1578479)

In this paper the operation of switching of tournaments is investigated. The main result is Theorem 5.2. A finite group is the automorphism group of some switching class of tournaments if and only if its Sylow 2-subgroups are cyclic or dihedral. It is a simple corollary that if \(G\) has cyclic or dihedral Sylow 2-subgroups then there is a switching class \(C\) of tournaments, with Aut(\(C)\simeq G\), having the property that every subgroup of \(G\) of odd order is the full automorphism group of a tournament in \(C\) (Corollary 6.10).