Forum Problem Lists Definitions FAQ

15.104 (2002)

Open

Let $n$ be a positive integer and let $w$ be a group word in the variables $x_1, x_2, \dots$. Suppose that a residually finite group $G$ satisfies the identity $w^n = 1$. Does it follow that the verbal subgroup $w(G)$ is locally finite?

Contributor: P. V. Shumyatsky

Progress

This is the Restricted Burnside Problem if $w = x_1$. A positive answer was obtained also in a number of other particular cases (P. V. Shumyatsky, Quart. J. Math., 51, no. 4 (2000), 523–528).

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.