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On the embedding of a group in a join of given groups

Published online by Cambridge University Press:  09 April 2009

P. Hall
P. Hall
Affiliation:
50, Impington Lane, Histon, Cambs, England
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1. In their fundamental paper of 1949, Higman, Neumann and Neumann proved for the first time that a countable group can always be embedded in some 2-generator group: [1], Theorem IV. Two kinds of improvement of this result have recently appeared. In [4], Theorem 2, Dark has shown that the embedding can always be made subnormally. On the other hand, in [2], Theorem 2.1, Levin has shown that the two generators can be given preassigned orders m > 1 and n > 2; and in [3], Miller and Schupp prove that the 2-generator group can also be made to satisfy several additional requirements, such as being complete and Hopfian.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 17 , Issue 4 , June 1974 , pp. 434 - 495
Copyright
Copyright © Australian Mathematical Society 1974

References

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