= Classification of finite simple groups
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= Classification of simple finite groups
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<Ciro Santilli> is very fond of this result: <the beauty of mathematics>.
How can so much complexity come out from so few rules?
How can the proof be so long (thousands of papers)?? Surprise!!
And to top if all off, the awesomely named <monster group> could have a relationship with <string theory> via the <monstrous moonshine>?
<all science is either physics or stamp collecting> comes to mind.
The classification contains:
* <cyclic groups>: infinitely many, one for each <prime> order. Non-prime orders are not simple. These are the only <Abelian> ones.
* <alternating groups> of order 4 or greater: infinitely many
* <groups of Lie type>: a contains several infinite families
* <sporadic groups>: 26 or 27 of them depending on definitions
\Video[https://www.youtube.com/watch?v=jhVMBXl5jTA]
{title=Simple Groups - Abstract Algebra by Socratica (2018)}
{description=Good quick overview.}