On the Free Product of Two Groups with an Amalgamated Subgroup of Finite Index in each Factor
- 1 September 1970
- journal article
- Published by JSTOR in Proceedings of the American Mathematical Society
- Vol. 26 (1) , 28-32
- https://doi.org/10.2307/2036796
Abstract
Let <!-- MATH $G = (A \ast B;U)$ --> where is finitely generated and of finite index in both and . We prove that is a finite extension of a free group iff and are both finite. In particular, this answers in the negative a question of W. Magnus as to whether or not can be free. Analogous results are obtained for tree products and HNN groups.
Keywords
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