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Visual Group Theory, Lecture 5.7: Finite simple groups
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Visual Group Theory, Lecture 5.7: Finite simple groups
A group is said to be simple if its only normal subgroups are itself and the identity. Using Sylow theorems, we can frequently conclude statemens such as "there are no simple groups of order k", for some fixed k. After we provide several examples of this in increasing difficulty, we state the classification theorem of finite simple groups. This was a monumental achievement, as the proof is about 15,000 pages long and took 50 years to complete. Finally, we conclude with light-hearted pun-filled love song titled "Finite simple group (of order two)", by the 5-member a cappella group appropriately (?) named The Klein Four.
A group is said to be simple if its only normal subgroups are itself and the identity. Using Sylow theorems, we can frequently conclude statemens such as "there are no simple groups of order k", for some fixed k. After we provide several examples of this in increasing difficulty, we state the classification theorem of finite simple groups. This was a monumental achievement, as the proof is about 15,000 pages long and took 50 years to complete. Finally, we conclude with light-hearted pun-filled love song titled "Finite simple group (of order two)", by the 5-member a cappella group appropriately (?) named The Klein Four.
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