Free products of topological groups with central amalgamation
TLDR
In this article, it was shown that GIIA H is a Hausdorff topological group with central amalgamation, and necessary and sufficient conditions for it to be a complete metric group, a Baire space, and a maximally almost periodic group.Abstract:
In Free products of topological groups with central amalgamation. I, we introduced the notion of amalgamated free product of topological groups and showed that if A is a common central closed subgroup of Hausdorff topological groups G and H, then the amalgamated free product G IIA H exists and is Hausdorff. In this paper, we give an alternative much shorter (but less informative) proof of this result. We then proceed to describe the properties of GIIA H. In particular, we find necessary and sufficient conditions for GIIA H to be a locally compact Hausdorff group, a complete metric group, and a maximally almost periodic group. Properties such as being a Baire space and connectedness are also investigated. In the case that G, H and A are k -groups, the topology of G II A H is fully described. A consequenceread more
Citations
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Journal ArticleDOI
Final group topologies, Kac-Moody groups and Pontryagin duality
TL;DR: In this paper, the Pontryagin duality theory for the classes of almost metrizable topological abelian groups and locally kω topological groups is studied. And the relation between countable projective limits and countable direct limits of locally k-abelian group topologies is explored.
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Final group topologies, Phan systems and Pontryagin duality
TL;DR: In this paper, the Pontryagin duality theory for the classes of almost metrizable topological abelian groups and locally k-omega topological groups is studied.
Journal ArticleDOI
Free products of topological groups with amalgamation. II.
Elyahu Katz,Sidney A. Morris +1 more
TL;DR: In this paper, it was shown that the free product with amalgamation of Hausdorff topological groups exists and is Haus-dorff if and only if the subgroup being amalgamated is central or if all groups concerned are kω and the amalgamation subgroup is compact.
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Free products with amalgamation over central C*-subalgebras
Kristin Courtney,Tatiana Shulman +1 more
TL;DR: In this paper, the authors generalize Korchagin's result that amalgamated free products of commutative C*-algebras are RFD to the case of a trivial amalgam.
References
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Book
Combinatorial Group Theory
Roger C. Lyndon,Paul E. Schupp +1 more
TL;DR: In this article, the authors introduce the concept of Free Products with Amalgamation (FPAM) and Small Cancellation Theory over free products with amalgamation and HNN extensions.
Book ChapterDOI
Free topological groups
TL;DR: In this article, the authors show that the following properties are not preserved by passage to the free abelian group: normal, k- sequential, Frechet, Lindelof, paracompact, countably compact, sequentially compact, etc.
Journal ArticleDOI
An Essay on Free Products of Groups with Amalgamations
TL;DR: Free products of groups with amalgamated subgroups, first introduced by Schreier (1927) and generalized by Hanna Neumann (1948), are here redefined, studied and applied to a number of problems in abstract group theory as mentioned in this paper.