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Let $G = A *_C B$ be an amalgamated free product of groups.

My question is: suppose $C$ and $G$ are finitely generated, can we prove that so is $A$?

I've been trying to prove it by contradiction. Any suggestion?

Thanks...

  • 0
    Do you assume that $C \to A, C \to B$ are injective? (some authors do this)2010-10-02
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    I believe many people (including myself) assume $C\to A$ and $C\to B$ are injective when speaking about an amalgamated free product of groups; otherwise they (and I) say G is a pushout.2010-10-02

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