On topological filtrations of groups
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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.
KeywordsWeak geometric simple connectivity Quasi-simple filtration Finitely presented groups Solvable groups
Mathematics Subject ClassificationPrimary 20F16 20F24 Secondary 57M07
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