Forum Problem Lists Definitions FAQ

2.62 (1966)

Solved

If $G$ is a finite-dimensional vector space over a field and $\Gamma$ is a group of automorphisms of $G$ in which every element is stable, then the whole of $\Gamma$ is stable (E. Kolchin). Is Kolchin’s theorem true for spaces over skew fields?

Contributor: B. I. Plotkin

Progress

Yes, it is, if the characteristic of the skew field is zero or sufficiently large compared to the dimension of the space (H. Y. Mochizuki, Canad. Math. Bull., 21 (1978), 249–250).

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.