Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
MathSciNet review: 0263928
Full-text PDF

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20.52

Retrieve articles in all journals with MSC: 20.52

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