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Apr 30 at 20:20 comment added Jan Nienhaus @MoisheKohan you are of course correct in that these may not be actual amalgamated free products. I'm commiting to some abuse of terminology here, and any mention of amalgamated products should more accurately be read as 'pushout in groups', noting that this ia an amalgamated free product if the involved maps are injections
Apr 18 at 4:19 comment added Moishe Kohan You are mistaken about the definition of the amalgamated free product. This is not what van Kampen's theorem gives you.
Apr 18 at 2:39 history answered Jan Nienhaus CC BY-SA 4.0