Displaying similar documents to “Varieties of topological groups a survey”

Identifying and distinguishing various varieties of abelian topological groups

Carolyn E. McPhail, Sidney A. Morris

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A variety of topological groups is a class of (not necessarily Hausdorff) topological groups closed under the operations of forming subgroups, quotient groups and arbitrary products. The variety of topological groups generated by a class of topological groups is the smallest variety containing the class. In this paper methods are presented to distinguish a number of significant varieties of abelian topological groups, including the varieties generated by (i) the class of all locally...

On the Boffa alternative

B. Bajorska, O. Macedońska (2001)

Colloquium Mathematicae

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Let G* denote a nonprincipal ultrapower of a group G. In 1986 M.~Boffa posed a question equivalent to the following one: if G does not satisfy a positive law, does G* contain a free nonabelian subsemigroup? We give the affirmative answer to this question in the large class of groups containing all residually finite and all soluble groups, in fact, all groups considered in traditional textbooks on group theory.

On the foundations of k-group theory

W. F. Lamartin

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CONTENTSIntroduction................... 51. k-spaces.................... 62. k-groups.................... 14References..................... 32