1
vote
0answers
58 views

Is the Hilbert-Smith conjecture still unsolved?

Conjecture Let $G$ be a locally compact topological group. If $G$ has a continuous faithful group action on an $n$-manifold, then $G$ is a Lie group. Is this conjecture still unsolved? Is ...
1
vote
1answer
47 views

reference in Montgomery/ Zippin

In a paper, the authors use the reference [M–Z, Theorem in 4.13] where [M-Z] denote the book D. Montgomery and L. Zippin, Topological Transformation Groups. Interscience Publishers, New York–London, ...
11
votes
1answer
199 views

subgroup of connected locally compact group

I need a reference or a short proof for the following property: A nontrivial connected locally compact group $G$ contains an infinite abelian subgroup.
12
votes
1answer
559 views

Properties of Haar measure

Let $G$ be a locally compact group (but not discrete) and let $m$ be its left Haar measure. Is it true that $\forall \epsilon$ $\exists$ $C$ such that $C$ is a compact neighborhood of the identity and ...
4
votes
1answer
569 views

Reference request: Fourier and Fourier-Stieltjes algebras

I would like to learn the basic theory of Fourier algebras and Fourier-Stieltjes algebras. In particular, I want to know how these two objects are defined in the case of not necessarily abelian ...