Geodesic
Subgroups satisfying an identity in a~class of abstract groups
Sbornik. Mathematics, Tome 71 (1992) no. 2, pp. 371-386

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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. 
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     author = {Yu. V. Tishin},
     title = {Subgroups satisfying an identity in a~class of abstract groups},
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Yu. V. Tishin. Subgroups satisfying an identity in a~class of abstract groups. Sbornik. Mathematics, Tome 71 (1992) no. 2, pp. 371-386. http://geodesic.mathdoc.fr/item/SM_1992_71_2_a6/