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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On the free product of two groups with an amalgamated subgroup of finite index in each factor


Authors: A. Karrass and D. Solitar
Journal: Proc. Amer. Math. Soc. 26 (1970), 28-32
MSC: Primary 20.52
DOI: https://doi.org/10.1090/S0002-9939-1970-0263928-2
MathSciNet review: 0263928
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Abstract: Let $ G = (A \ast B;U)$ where $ U$ is finitely generated and of finite index $ \ne 1$ in both $ A$ and $ B$. We prove that $ G$ is a finite extension of a free group iff $ A$ and $ B$ are both finite. In particular, this answers in the negative a question of W. Magnus as to whether or not $ G$ can be free. Analogous results are obtained for tree products and HNN groups.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0263928-2
Keywords: Amalgamated products, generalized free products, tree products, HNN groups, finite extensions of free groups, free subgroups of finite index, free groups
Article copyright: © Copyright 1970 American Mathematical Society