Forum Problem Lists Definitions FAQ

13.10 (1995)

Solved

Is there a function $f : \mathbb{N} \to \mathbb{N}$ such that, for every soluble group $G$ of derived length $k$ generated by a set $A$, the validity of the identity $x^4 = 1$ on each subgroup generated by at most $f(k)$ elements of $A$ implies that $G$ is a group of exponent 4?

Contributor: V. V. Bludov

Progress

No, there is not (G. S. Deryabina, A. N. Krasil’nikov, Siberian Math. J., 44, no. 1 (2003), 58–60).

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.