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An Existence Theorem for Generalized Direct Products with Amalgamated Subgroups

Published online by Cambridge University Press:  20 November 2018

C. Y. Tang
C. Y. Tang*
Affiliation:
Illinois Institute of Technology, Chicago
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Generalized direct products with amalgamated subgroups were introduced by B. H. Neumann and Hanna Neumann in their joint paper (4). In general, we call a given collection of groups with specified subgroups amalgamated an amalgam of groups; if all groups are abelian we speak of an abelian amalgam. The group freely generated by the amalgam is called the abelian free sum of the amalgam provided it contains the amalgam isomorphically. The free abelian sum need not exist. Hence one of the problems is to find necessary and sufficient conditions for its existence.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 75 - 82
Copyright
Copyright © Canadian Mathematical Society 1966

References

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