[math-fun] Non-isomorphic finite simple groups of the same order
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. Question: How many such orders are there? Infinitely many? --Dan Sometimes the brain has a mind of its own.
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
Related question on MathOverflow: http://mathoverflow.net/questions/34424/number-of-finite-simple-groups-of-gi... AA On Sun, Jul 17, 2011 at 6:03 PM, Fred W. Helenius <fredh@ix.netcom.com>wrote:
On 7/17/2011 8:06 PM, Dan Asimov wrote:
According to this website:< http://www.madore.org/~david/** math/simplegroups.html<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
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participants (3)
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Alon Amit -
Dan Asimov -
Fred W. Helenius