17 Jul
2011
17 Jul
'11
7:04 p.m.
On 7/17/2011 8:06 PM, Dan Asimov wrote:
According to this website:< http://www.madore.org/~david/math/simplegroups.html>, the smallest order for which there are more than one isomorphism class of finite simple groups is 2160.
That's 20160.
Question: How many such orders are there? Infinitely many?
There are infinitely many, since the finite groups of Lie type B_n(q) and C_n(q) are simple for n > 1 and q a prime power, have the same order, and are not isomorphic for n > 2 and q an odd prime power. On the page you mention, the first groups of this sort are listed as (lie b 3 3) and (lie c 3 3), both of order 4585351680. -- Fred W. Helenius fredh@ix.netcom.com