Abstract
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.
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Acknowledgments
D.E. Otera was partially supported by the Research Council of Lithuania Grant No. MIP-046/2014/LSS-580000-446 (Researcher teams’ projects). F.G. Russo was supported in part by NRF (South Africa) for the Grant No. 93652 and in part from the Launching Grant No. 459235 of the University of Cape Town (South Africa). We thank V. Poénaru, C. Tanasi and L. Funar for useful discussions and comments.
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Otera, D.E., Russo, F.G. On topological filtrations of groups. Period Math Hung 72, 218–223 (2016). https://doi.org/10.1007/s10998-016-0129-0
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DOI: https://doi.org/10.1007/s10998-016-0129-0