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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On the finitely generated subgroups of an amalgamated product of two groups

Author: R. G. Burns
Journal: Trans. Amer. Math. Soc. 169 (1972), 293-306
MSC: Primary 20F05
MathSciNet review: 0372043
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Abstract: Sufficient conditions are found for the free product $G$ of two groups $A$ and $B$ with an amalgamated subgroup $U$ to have the properties (1) that the intersection of each pair of finitely generated subgroups of $G$ is again finitely generated, and (2) that every finitely generated subgroup containing a nontrivial subnormal subgroup of $G$ has finite index in $G$. The known results that Fuchsian groups and free products (under the obvious conditions on the factors) have properties (1) and (2) follow as instances of the main result.

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Keywords: Amalgamated product, generalized free product, malnormal subgroup, subnormal subgroup, finitely generated intersection property, Kuroš rewriting process, Schreier system, compatible regular extended Schreier system, double ended coset
Article copyright: © Copyright 1972 American Mathematical Society