Incoming links: Monster group
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
Quotient of a subgroup H of G by a normal subgroup of the subgroup H.
That normal subgroup does not have have to be a normal subgroup of G.
As an overkill example, the happy family are subquotients of the monster group, but the monster group is simple.