Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

The recent paper, "Aftermath," by Peter Cameron (arXiv:1111.4050v1), contains this remark concerning the classification of the finite simple groups:

The Classification of Finite Simple Groups [16] is the greatest collaborative effort ever in mathematics, running to about 15000 journal pages. (Ironically, although the theorem was announced in 1980, the proof contained a gap which has only just been filled.)

Can someone explain (at a high level) what was the gap and who filled it? (Cameron gives no reference.) Thanks!

share|cite|improve this question
I believe it may be a reference to the classification of quasi-thin groups, filled by Aschbacher and Smith around 2004. – Arturo Magidin Nov 28 '11 at 2:09
Thank you, Arturo! After reading a bit on quasithin groups, I see that you are surely correct. – Joseph O'Rourke Nov 28 '11 at 14:01
up vote 9 down vote accepted

Answering as a CW so the question will not appear as unanswered.

I believe it may be a reference to the classification of quasithin groups; this was filled by Aschbacher and Smith in a series of papers around 2004.

The fact that this was a gap that needed to be filled only became apparent as the proof was being organized for re-publication (in the AMS book series).

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.