On topological filtrations of groups

The (weak) geometric simple connectivity and the quasi-simple filtration are topological notions of manifolds, which may be defined for discrete groups too. It turns out that they are equivalent for finitely presented groups, but the main problem is the absence of examples of groups which do not sat...

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Bibliographic Details
Published inPeriodica mathematica Hungarica Vol. 72; no. 2; pp. 218 - 223
Main Authors Otera, Daniele Ettore, Russo, Francesco G.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.06.2016
Subjects
Mathematics
Mathematics and Statistics
Weak geometric simple connectivity
Solvable groups
Finitely presented groups
Quasi-simple filtration
Primary 20F16
Secondary 57M07
20F24
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Summary:The (weak) geometric simple connectivity and the quasi-simple filtration are topological notions of manifolds, which may be defined for discrete groups too. It turns out that they are equivalent for finitely presented groups, but the main problem is the absence of examples of groups which do not satisfy them. In this note we study some algebraic classes of groups with respect to these properties.
ISSN:0031-5303
1588-2829
DOI:10.1007/s10998-016-0129-0