McKay, BrendanWanless, IanZhang, Xiande2015-12-101063-8539http://hdl.handle.net/1885/58634We prove quadratic upper bounds on the order of any autotopism of a quasigroup or Latin square, and hence also on the order of any automorphism of a Steiner triple system or 1-factorization of a complete graph. A corollary is that a permutation σ chosen201410.1002/jcd.213892015-12-10