Forum Problem Lists Definitions FAQ

15.59 (2002)

Open

Does there exist a profinite group $G$ that is not free but can be represented as a projective limit $G = \varprojlim(G/N_\alpha)$, where all the $G/N_\alpha$ are free profinite groups of finite ranks?

The finiteness condition on the ranks of the $G/N_\alpha$ is essential. Such a group $G$ cannot satisfy the first axiom of countability (O. V. Mel’nikov, Dokl. AN BSSR, 24, no. 11 (1980), 968–970 (Russian)).

Contributor: O. V. Mel’nikov

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.