Forum Problem Lists Definitions FAQ

14.14 (1999)

Open

(C. C. Edmunds, G. Rosenberger). We call a pair of natural numbers $(k, m)$ admissible if in the derived subgroup $F'_2$ of a free group $F_2$ there is an element $w$ such that the commutator length of the element $w^m$ is equal to $k$. Find all admissible pairs.

Contributor: V. G. Bardakov

Progress

It is known that every pair $(k, 2)$, $k \geqslant 2$, is admissible (V. G. Bardakov, Algebra and Logic, 39 (2000), 224–251).

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.