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MSC 2010: 30C60A more general version of Hilbert's fifth problem, called the Hilbert-Smith conjecture, asserts that among all locally compact topological groups only Lie groups can act effectively on finite-dimensional manifolds. We give a solution of the Hilbert-Smith Conjecture for K - quasiconformal groups acting on domains in the extended n - dimensional Euclidean space.

Idempotents and the multiplicative group of some totally bounded rings

Mohamed A. Salim, Adela Tripe (2011)

Czechoslovak Mathematical Journal

In this paper, we extend some results of D. Dolzan on finite rings to profinite rings, a complete classification of profinite commutative rings with a monothetic group of units is given. We also prove the metrizability of commutative profinite rings with monothetic group of units and without nonzero Boolean ideals. Using a property of Mersenne numbers, we construct a family of power $2^{ℵ_{0}}$ commutative non-isomorphic profinite semiprimitive rings with monothetic group of units.

Kompakt definierbare topologische Gruppen.

Herbert Abels (1972)

Mathematische Annalen

Large scale Sobolev inequalities on metric measure spaces and applications.

R. Tessera (2008)

Revista Matemática Iberoamericana

Left and right on locally compact groups.

Giovanna Carcano (1996)

Collectanea Mathematica

Let G be a locally compact, non-compact group and f a function defined on G; we prove that, if f is uniformly continuous with respect to the left (right) structure on G and with a power integrable with respect to the left (right) Haar measure on G, then f must vanish at infinity. We prove that left and right cannot be mixed.