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Permutational products of groups

Published online by Cambridge University Press:  09 April 2009

B. H. Neumann
B. H. Neumann
Affiliation:
The University, Manchester
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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.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 1 , Issue 3 , August 1960 , pp. 299 - 310
Copyright
Copyright © Australian Mathematical Society 1960

References

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