scholarly journals Local compactness and local invariance of free products of topological groups

1976 ◽  
Vol 35 (1) ◽  
pp. 21-27 ◽  
Author(s):  
Sidney A. Morris
Keyword(s):  
Topological Groups ◽  
Free Products ◽  
Local Compactness ◽  
Local Invariance

scholarly journals Free products of topological groups with amalgamation. II

1985 ◽  
Vol 120 (1) ◽  
pp. 123-130 ◽  
Author(s):  
Elyahu Katz ◽  
Sidney Morris
Keyword(s):  
Topological Groups ◽  
Free Products

scholarly journals Free products of topological groups with a closed subgroup amalgamated

1986 ◽  
Vol 40 (3) ◽  
pp. 414-420 ◽  
Author(s):  
Peter Nickolas
Keyword(s):  
Topological Group ◽  
Free Product ◽  
Closed Subgroup ◽  
Countable Family ◽  
Topological Groups ◽  
Free Products ◽  
Dense Image ◽  
Amalgamated Free Product

AbstractIt 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.

scholarly journals Free products of topological groups

1971 ◽  
Vol 4 (1) ◽  
pp. 17-29 ◽  
Author(s):  
Sidney A. Morris
Keyword(s):  
Topological Group ◽  
Free Product ◽  
Quotient Group ◽  
Closed Subgroup ◽  
Topological Product ◽  
Almost Periodic ◽  
Topological Groups ◽  
Free Products ◽  
Free Topological Group ◽  
Product Of Groups

In this note the notion of a free topological product Gα of a set {Gα} of topological groups is introduced. It is shown that it always exists, is unique and is algebraically isomorphic to the usual free product of the underlying groups. Further if each Gα is Hausdorff, then Gα is Hausdorff and each Gα is a closed subgroup. Also Gα is a free topological group (respectively, maximally almost periodic) if each Gα is. This notion is then combined with the theory of varieties of topological groups developed by the author. For a variety of topological groups, the -product of groups in is defined. It is shown that the -product, Gα of any set {Gα} of groups in exists, is unique and is algebraically isomorphic to the usual varietal product. It is noted that the -product of Hausdorff groups is not necessarily Hausdorff, but is if is abelian. Each Gα is a quotient group of Gα. It is proved that the -product of free topological groups of and projective topological groups of are of the same type. Finally it is shown that Gα is connected if and only if each Gα is connected.

scholarly journals Free products of topological groups: Corrigendum

1975 ◽  
Vol 12 (3) ◽  
pp. 480-480
Author(s):  
Sidney A. Morris
Keyword(s):  
Topological Groups ◽  
Free Products ◽  
Special Case

Professor Edward T. Ordman has pointed out to the author that the proof of Theorem 2.2 in [2] is incorrect. The theorem is, in fact, correct and was proved by Graev [1] The incorrect proof presented in my paper has been modified by Ordman [3] to provide a much simpler proof than Graev's in a special case.

scholarly journals Torsion-free word hyperbolic groups are noncommutatively slender

2016 ◽  
Vol 26 (07) ◽  
pp. 1467-1482 ◽  
Author(s):  
Samuel M. Corson
Keyword(s):  
Free Subgroup ◽  
Hyperbolic Groups ◽  
Topological Groups ◽  
Free Products ◽  
Finitely Presented Groups ◽  
Word Hyperbolic Groups ◽  
Hawaiian Earring ◽  
Free Word ◽  
Finitely Presented ◽  
Torsion Free

In this paper, we prove the claim given in the title. A group [Formula: see text] is noncommutatively slender if each map from the fundamental group of the Hawaiian Earring to [Formula: see text] factors through projection to a canonical free subgroup. Higman, in his seminal 1952 paper [Unrestricted free products and varieties of topological groups, J. London Math. Soc. 27 (1952) 73–81], proved that free groups are noncommutatively slender. Such groups were first defined by Eda in [Free [Formula: see text]-products and noncommutatively slender groups, J. Algebra 148 (1992) 243–263]. Eda has asked which finitely presented groups are noncommutatively slender. This result demonstrates that random finitely presented groups in the few-relator sense are noncommutatively slender.

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