On quasi-thin association schemes with odd number of points

Let (X, R) be an association scheme in the sense of P.-H. Zieschang (1996, "An Algebraic Approach to Association Schemes," Lecture Notes in Mathematic s, Vol. 1628, Springer, New York/Berlin), where X is a finite set and R is a partition of X x X. We say that (X, R) is quasi-thin if each element of R has a valency of at most two. In this paper we focus on quasi-thin associa tion schemes with an odd number of points and obtain that (X, R) has a regu lar automorphism group when n(O)((R))(0) is square-free, (C) 2001 Academic Press.