Forum Problem Lists Definitions FAQ

11.57 (1990)

Solved

An upper composition factor of a group $G$ is a composition factor of some finite quotient of $G$. Is there any restriction on the set of non-abelian upper composition factors of a finitely generated group?

Contributor: A. Mann, D. Segal

Progress

There are no restrictions: any set of non-abelian finite simple groups can be the set of upper composition factors of a 63-generator group; if we allow the group to have also abelian upper composition factors, the number of generators can be reduced to 3 (D. Segal, Proc. London Math. Soc. (3), 82 (2001), 597–613).

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.