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Lifting amalgamated sums and other colimits of groups and topological groups

Published online by Cambridge University Press:  24 October 2008

Ronald Brown  and
Philip R. Heath
Ronald Brown
Affiliation:
Department of Pure Mathematics, University College of North Wales, Bangor, Gwynedd LL57 2UW
Philip R. Heath
Affiliation:
Department of Mathematics, Memorial University of Newfoundland, St John's, Newfoundland A1C 5S7, Canada
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Extract

Suppose a group H is given as a free product with amalgamation

determined by groups A0, A1, A2 and homomorphisms α1: A0 → A1, α2: A0 → A2. Thus H may be described as the quotient of the free product A * A2 by the relations i1 α1 (α0) = i2α2 (α0) for all α0 ∈ A0, where i1, i2 are the two injections of A1, A2 into A1 * A2. We do not assume that α1, α2 are injective, so the canonical homomorphisms α′i: Ai → H, i = 0,1,2, also need not be injective.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 102 , Issue 2 , September 1987 , pp. 273 - 280
Copyright
Copyright © Cambridge Philosophical Society 1987

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References

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