Forum Problem Lists Definitions FAQ

21.7 (2026)

Open

(Well-known problem). A finite group $G$ is called an IYB-group if it is isomorphic to the permutation group of a finite involutive non-degenerate set-theoretic solution of the Yang–Baxter equation, or equivalently, $G$ is isomorphic to the multiplicative group of a finite left brace. Assume that the Sylow subgroups of a finite soluble group $G$ are IYB-groups. Is $G$ an IYB-group?

Contributor: A. Ballester-Bolinches

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.