Abstract:
In this paper the technique of group action on a tree is used to obtain solutions of the following problems. Suppose that the group $G$ is a free construction.
1. Describe the normal subgroups of $G$ not containing non-Abelian free subgroups.
2. Describe the normal subgroups $A$ and $B$ of $G$ if the mutual commutator subgroup $[A,B]$ does not contain non-Abelian free subgroups.
The results are applied to groups obtained by using a sequence of operations of taking $HNN$-extensions and forming free products with amalgamation.
Bibliography: 16 titles.