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JOURNALS // Matematicheskii Sbornik // Archive

Mat. Sb. (N.S.), 1985 Volume 126(168), Number 3, Pages 377–396 (Mi sm1942)

This article is cited in 4 papers

Normal subgroups of free constructions

Yu. V. Tishin


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.

UDC: 512.54

MSC: 20E06, 20E07

Received: 30.01.1984


 English version:
Mathematics of the USSR-Sbornik, 1986, 54:2, 367–385

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