Amalgamated free product

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This article describes a product notion for groups. See other related product notions for groups.

Definition

Definition with strict common subgroup

Let G_1 and G_2 be two groups, and let H be a group with an injective homomorphism to both G_1 and G_2. Then the amalgamated free product of G_1 and G_2 via H is defined as the quotient of the free product of G_1 and G_2, by the relation of the H in G_1 being the same as the H in G_2.

Definition of weaker notion (pushout version)

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