[FOM] classification of finite simple groups

[Francis Davey]

On 1 Nov 2008, at 21:03, Michael J Barany wrote:

> Hi all,
>
> In my abstract algebra class a few years back, we were told that  
> algebrists
> were pretty confident that the classification of finite simple  
> groups had been
> solved, and that all that remained was to do the huge project of  
> writing up
> the proofs in a single multi-volume work and filling in the gaps and  
> cleaning
> up notation and the like.  I heard recently from some algebrists  
> that a new
> class of groups had just been found not too long ago, and that now  
> many are
> doubting whether the classification is finished after all.  I  
> haven't pursued
> the references for this much, and it occurs to me that I wouldn't  
> really know
> where to start, but it came up in a conversation today with another  
> FOMer, and
> we thought we'd ask the list if anyone knew of any references, or  
> could
> substantiate this rumor.


Could you be thinking of the improvement in the theorem (to cover  
quasithin groups) by Michael Aschbacher and others a few years ago?  
I'm not sure if the time scale is quite right, see:

http://www.ams.org/notices/200407/fea-aschbacher.pdf

Of course the classification of finite simple groups is not the same  
thing as the classification of finite groups - something which much of  
the popular literature about the classification fails to make clear.  
My understanding is that the group extension problem is still thought  
of as difficult.

-- 

Francis Davey