Forum Problem Lists Definitions FAQ

14.70 (1999)

Open

A group $G$ is called $n$-Engel if it satisfies the identity $[x, y, \dots, y] = 1$, where $y$ is taken $n$ times. Are there non-nilpotent finitely generated $n$-Engel groups?

Contributor: B. I. Plotkin

Progress

Comment of 2017: For $n = 2, 3, 4$, finitely generated $n$-Engel groups are nilpotent. A course of lectures devoted to constructing non-nilpotent finitely generated $n$-Engel groups for sufficiently large $n$ is given by E. Rips and is available on the Internet.

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.