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 | References | Similar Articles | Additional Information
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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Additional Information
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