All Questions

What is the easiest way to show that a compact hausdorff topological group is a closed subgroup of a product of finite dimensional Lie groups? Here are the relevant definitions: Definition: (compact ...

This question concerns the following lemma of this paper: Lemma 2. Let $\mathcal X_1,\ldots,\mathcal X_n$ be classes of finite groups closed with respect to normal subgroups and subdirect products ...

Let $G$ be a compact group. Let $\mathcal N$ be a family of closed normal subgroups of nilpotency class at most $k$. Assume that $\mathcal N$ is closed under finite intersections and $\bigcap_{N\in\...

Let $G$ be a simple (i.e. every proper normal subgroup is discrete) simply connected compact Lie group. Define the degree of $k$-nilpotence of $G$ to be the Haar measure of the set $$\{(x_1,\dotsc,x_{...

I am reading Bredon's Introduction to compact transformation groups, and came across the following result and proof on page 34: Even though he writes "Recall our standing assumption that $X$ is ...

I assume all tolpological groups here to be Hausdorff. A group is called locally finite if every finitely generated subgroup is finite. What can be said about a locally finite compact group? Must it ...