Forum Problem Lists Definitions FAQ

18.52 (2014)

Solved

Is every finite simple group generated by two elements of prime-power orders $m, n$? (Here numbers $m, n$ may depend on the group.) The work of many authors shows that it remains to verify this property for a small number of finite simple groups.

Contributor: J. Krempa

Progress

Yes, it is (mod CFSG); moreover, every finite simple group is generated by an involution and an element of prime order (C. S. H. King, J. Algebra, 478 (2017), 153–173).

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.