4
$\begingroup$

I am reading an introductory material about topological groups and the question in the tittle comes up. Due this Proposition

Proposition. A locally compact Hausdorff topological group $G$ is compact, if and only if, $\mu(G)<+\infty\qquad $ ($\mu$ is the Haar measure of $G$).

it is enough to know what are the groups $G$ for which $G/Z$, where $Z$ is the center of $G$, is a compact group. Are those groups well-known ?

  • 0
    Hi Theo, thanks a lot. I first thought about some matriz groups but I wrong convinced myself that they were compacts. The collection of example you provided let more clear that is in pratical very hard to classify all the groups with that property.2011-06-03

1 Answers 1