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# Free products with amalgamation and $\lowercase{p}$-adic Lie groups

Published:1998-12-01
Printed: Dec 1998
• D. D. Long
• A. W. Reid
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## Abstract

Using the theory of $p$-adic Lie groups we give conditions for a finitely generated group to admit a splitting as a non-trivial free product with amalgamation. This can be viewed as an extension of a theorem of Bass.
 MSC Classifications: 20E06 - Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations