Displaying similar documents to “Some remarks on the ends of groups.”

On Parabolic Subgroups and Hecke Algebras of some Fractal Groups

Bartholdi, Laurent, Grigorchuk, Rostislav (2002)

Serdica Mathematical Journal

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* The authors thank the “Swiss National Science Foundation” for its support. We study the subgroup structure, Hecke algebras, quasi-regular representations, and asymptotic properties of some fractal groups of branch type. We introduce parabolic subgroups, show that they are weakly maximal, and that the corresponding quasi-regular representations are irreducible. These (infinite-dimensional) representations are approximated by finite-dimensional quasi-regular representations....

On three-dimensional space groups.

Conway, John H., Delgado Friedrichs, Olaf, Huson, Daniel H., Thurston, William P. (2001)

Beiträge zur Algebra und Geometrie

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On the isoperimetry of graphs with many ends

Christophe Pittet (1998)

Colloquium Mathematicae

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Let X be a connected graph with uniformly bounded degree. We show that if there is a radius r such that, by removing from X any ball of radius r, we get at least three unbounded connected components, then X satisfies a strong isoperimetric inequality. In particular, the non-reduced l 2 -cohomology of X coincides with the reduced l 2 -cohomology of X and is of uncountable dimension. (Those facts are well known when X is the Cayley graph of a finitely generated group with infinitely many ends.) ...

On residually finite groups and their generalizations

Andrzej Strojnowski (1999)

Colloquium Mathematicae

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The paper is concerned with the class of groups satisfying the finite embedding (FE) property. This is a generalization of residually finite groups. In [2] it was asked whether there exist FE-groups which are not residually finite. Here we present such examples. To do this, we construct a family of three-generator soluble FE-groups with torsion-free abelian factors. We study necessary and sufficient conditions for groups from this class to be residually finite. This answers the questions...

Basic results on braid groups

Juan González-Meneses (2011)

Annales mathématiques Blaise Pascal

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These are Lecture Notes of a course given by the author at the French-Spanish School , held in Pau (France) in October 2009. It is basically an introduction to distinct approaches and techniques that can be used to show results in braid groups. Using these techniques we provide several proofs of well known results in braid groups, namely the correctness of Artin’s presentation, that the braid group is torsion free, or that its center is generated by the full twist. We also recall some...