Forum Problem Lists Definitions FAQ

15.18 (2002)

Solved

A group is hereditarily just infinite if it is residually finite and all of its non-trivial normal subgroups are just infinite.
$\qquad$ a) Do there exist finitely generated hereditarily just infinite torsion groups?
$\qquad$ b) Is every finitely generated hereditarily just infinite group necessarily linear?
A positive answer to the question b) would imply a negative answer to a).

Contributor: L. Bartholdi, R. I. Grigorchuk, Z. Šuniḱ

Progress

a) Yes, such groups exist (M. Ershov, A. Jaikin-Zapirain, J. Reine Angew. Math., 677 (2013), 71–134).
b) No, not every (M. Ershov, A. Jaikin-Zapirain, J. Reine Angew. Math., 677 (2013), 71–134).

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.