- #1

Oxymoron

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*free product*of [itex]G_1[/itex] and [itex]G_2[/itex] amalgamated over A. Denote this free product by [itex]G_1 \star_A G_2[/itex].

Q1: Now I have read that you can associated a tree, T, to [itex]G_1 \star_A G_2[/itex]. Is this true?

Q2: What is [itex]\mbox{Aut}(\Gamma)[/itex]? Is it the collection of all isomorphic homomorphisms [itex]\varphi[/itex] from the tree to itself?

Q3: Does it make sense to think that there should be a homomorphism from the free product [itex]G_1 \star_A G_2[/itex] to [itex]\mbox{Aut}(\Gamma)[/itex]?