Forum Problem Lists Definitions FAQ

4.5 (1973)

Partially Solved

a) (J. Milnor). Is it true that an arbitrary finitely generated group has either polynomial or exponential growth?
b) Is it true that an arbitrary finitely presented group has either polynomial or exponential growth?
c) Is it true that every finitely generated group with undecidable word problem has exponential growth?

Contributor: S. I. Adian

Progress

a) No.

c) No (R. I. Grigorchuk, Soviet Math. Dokl., 28 (1983), 23–26).

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.