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Transactions of the American Mathematical Society

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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
DOI: https://doi.org/10.1090/S0002-9947-1972-0372043-5
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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1972-0372043-5
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

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