Forum Problem Lists Definitions FAQ

1.35 (1965)

Partially Solved

A group is called pro-orderable if every partial ordering of the group extends to a linear ordering.
$\qquad$ a) Is the wreath product of two arbitrary pro-orderable groups again pro-orderable?
$\qquad$ b) (A. I. Mal’cev). Is every subgroup of a pro-orderable group again pro-orderable?
$\qquad$ c) (A. I. Mal’cev, L. Fuchs). Do there exist simple pro-orderable groups?

Contributor: M. I. Kargapolov

Progress

For a) and b), not always, in both cases (V. M. Kopytov, Algebra i Logika, 5, no. 6 (1966), 27–31 (Russian)).

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.