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Free products of topological groups with a closed subgroup amalgamated

Part of: Topological and differentiable algebraic systems Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

Peter Nickolas
Peter Nickolas
Affiliation:
Department of Mathematics, University of Queensland, St. Lucia 4067, Australia
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Abstract

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It is shown that if {Gn: n = 1, 2,…} is a countable family of Hausdorff kω-topological groups with a common closed subgroup A, then the topological amalgamated free product *AGn exists and is a Hausdorff kω-topological group with each Gn as a closed subgroup. A consequence is the theorem of La Martin that epimorphisms in the category of kω-topological groups have dense image.

MSC classification

Secondary: 22A05: Structure of general topological groups 20E06: Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 40 , Issue 3 , June 1986 , pp. 414 - 420
Copyright
Copyright © Australian Mathematical Society 1986

References

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