Bryant, DarrynBuchanan, MelindaWanless, Ian2015-12-070012-365Xhttp://hdl.handle.net/1885/20873We determine necessary and sufficient conditions for the existence of a quasigroup of order n having an automorphism consisting of a single cycle of length m and n - m fixed points, and having any combination of the additional properties of being idempotent, unipotent, commutative, semi-symmetric or totally symmetric. Quasigroups with such additional properties and symmetries are equivalent to various classes of triple systems.Keywords: System theory; Diagonally cyclic; Latin square; Mendelsohn triple system; Quasigroup; Semi-symmetric; Steiner triple system; Totally symmetric; Equivalence classes Diagonally cyclic; Latin square; Mendelsohn triple system; Quasigroup; Semi-symmetric; Steiner triple system; Totally symmetric200910.1016/j.disc.2008.01.0202016-02-24