Representations of free groups on rational line Q

Abstract

A.M.W. Glass and S. H. McCleary have given the 2-transitive representation of the countable free l-group Fη (1 < η ⩽ ωo) (1<η⩽ω0). In this paper we shall give the highly ordered-transitive representation of countable free groups on the rational line Q, which generalizes their results. As applications, we obtain the highly ordered-transitive representation for the direct product of countable free groups,and the inverse limit of countable free groups must be an action on the set Q.