Permutational products of groups

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Abstract
We deal with questions about the possible embeddings of two given groups A and B in a group P such that the intersection of A and B is a given subgroup H. The data, consisting of the “constituents” A and B with the “amalgamated” subgroup H, form an amalgam.1 According to a classical theorem of Otto Schreier [5], every amalgam of two groups can be embedded in a group F, the “free product of A and B with amalgamated subgroup H” or the “generalized free product” of the amalgam. This has the property that every group P in which the amalgam is embedded and which is generated by the amalgam, is a homomorphic image of it. Hence theorems on the existence of certain embedding groups P can be interpreted also as theorems on the existence of certain normal subgroups of F.

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