Forum Problem Lists Definitions FAQ

19.107 (2018)

Open

Let $\mathcal{AE}$ be the smallest class of locally compact groups such that (1) $\mathcal{AE}$ contains the compact groups and the discrete amenable groups; (2) $\mathcal{AE}$ is closed under taking closed subgroups, Hausdorff quotients, directed unions of open subgroups, and group extensions.
Is every amenable locally compact group an element of $\mathcal{AE}$?

(A negative answer would follow from a positive answer to 19.21.)

Contributor: P. Wesolek

Comments

All comments are the responsibility of the user. Comments appearing on this page are not verified for correctness. Please keep posts mathematical and on topic. If you want to submit a proof (or a partial proof), please use the dedicated proof submission form rather than posting it in the comments.
Order by newest first or oldest first.

No comments yet. Be the first to comment.

Proof claims

Proof claims are the responsibility of the submitter. Appearance here does not mean the claim has been checked for mathematical correctness. Moderators only screen for spam, abuse, and obviously low-effort submissions.

No proof claims yet.