M. Gromov has shown that any two finitely generated groups Γ and Λ are quasi-isometric if and only if they admit a topological coupling, i.e., a commuting pair of proper continuous cocompact actions Γ y X x Λ on a locally compact Hausdorff space. This result is extended here to all (compactly generated) locally compact second-countable groups. In his seminal monograph on geometric group theory ...

in this paper, we compute the number of fuzzy subgroups of some classes of non-abeilan groups. explicit formulas are givenfor dihedral groups $d_{2n}$, quasi-dihedral groups $qd_{2^n}$, generalized quaternion groups $q_{4n}$ and modular $p$-groups $m_{p^n}$.

where f is a continuous function of compact support onGwith values in V . This is not quite a trivial matter. If V is assumed to be complete, a definition by Riemann sums works quite well, but this is an unnecessarily strong requirement. The natural condition on V seems to be that it be quasi-complete, a somewhat technical but nonetheless valuable condition. Continuous representations of a loca...

where f is a continuous function of compact support onGwith values in V . This is not quite a trivial matter. If V is assumed to be complete, a definition by Riemann sums works quite well, but this is an unnecessarily strong requirement. The natural condition on V seems to be that it be quasi-complete, a somewhat technical but nonetheless valuable condition. Continuous representations of a loca...

Suppose G is a hyperbolic group whose boundary ∂∞G has topological dimension k. If ∂∞G is quasi-symmetrically homeomorphic to an Ahlfors kregular metric space, then, modulo a finite normal subgroup, G is isomorphic to a uniform lattice in the isometry group Isom(Hk+1) of hyperbolic (k+1)-space.