A Note on Some Tricyclic Steiner Triple Systems

摘要

A Steiner triple system of order v, STS(v), is a pair (S, β), where S is a set of v points and β is a collection of three element subsets of S, called blocks such that any pair of distinct points of S is contained in precisely one block of β. An automorphism of a Steiner triple system, (S, β), is a permutation of S which maps β onto β. We show that no Steiner triple system admits an automorphism consisting of three cycles with two cycles of equal length and one larger cycle.