free product with amalgamated subgroup

Definition 1.

Let Gk, k=0,1,2 be groups and ik:G0Gi, k=1,2 be monomorphismsMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath. The free productMathworldPlanetmath of G1 and G2 with amalgamated subgroupMathworldPlanetmathPlanetmath G0, is defined to be a group G that has the following two properties

  1. 1.

    there are homomorphismsMathworldPlanetmathPlanetmathPlanetmathPlanetmath jk:GkG, k=1,2 that make the following diagram commute