Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-14T23:12:14.046Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[1]Brown, R. and Hardy, J. P. L., “Subgroups of free topological groups and free topological products of topological groups”, J. London Math. Soc. (2) 10 (1975), 431–440.CrossRefGoogle Scholar
[2]Elyahu Katz and Sidney A. Morris, “Free products of topological groups with amalgamation”, to appear.Google Scholar
[3]Elyahu Katz and Sidney A. Morris, “Free products of topological groups with amalgamation. II”, to appear.Google Scholar
[4]Katz, Eli and Morris, Sidney A., “Free products of kω-topological groups with normal amalgamation”, Topology Appl. 15 (1983), 189–196.CrossRefGoogle Scholar
[5]Kurosh, A. G., Kivshits, A. Kh. and Schul'geifer, E. G., “The foundations of the theory of categories”, Russian Math. Surveys 15 (No. 6) (1960), 1–46.CrossRefGoogle Scholar
[6]La Martin, W. F., “On the foundations of k-group theory”, Dissertationes Math. (Rozprawy Mat.) 146 (1977).Google Scholar
[7]Madison, B. L., Congruences in topological semigroups (Second Florida Symposium on Automata and Semigroups, University of Florida (1971), Part II).Google Scholar
[8]Neumann, B. H., “An essay on free products of groups with amalgamations”, Philos. Trans. Royal Soc. London (A) 246 (1954), 503–554.Google Scholar
[9]Nummela, Eric C., “On epimorphisms of topological groups”, General Topology and Appl. 9 (1978), 155–167.CrossRefGoogle Scholar
[10]Ordman, Edward T., “Free k-groups and free topological groups”, General Topology and Appl. 5 (1975), 205–219.CrossRefGoogle Scholar
[11]Thomas, Barbara V. Smith, Categories of topological groups (Presented to Second Symposium on Categorical Topology, University of Capetown (1976), Memphis State University Report 76–16).Google Scholar