Subgroups satisfying an identity in a class of abstract groups

A description is obtained of the subgroups of groups acting on a tree that do not contain nonabelian free subgroups; it is a new interpretation of a result of Bass. The author considers the class $\mathscr G$ consisting of all groups constructive from cyclic groups using amalgamated free products and HNN-extensions, with certain restrictions. A description is obtained of all the subgroups of groups in $\mathscr G$ that satisfy identities, and it is shown that the groups in $\mathscr G$ satisfy the Tits alternative. The proof uses the techniques of group actions on trees.