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by Ciro Santilli (@cirosantilli, 37)

Simple group

 ... Area of mathematics Algebra Group Subgroup Quotient group Normal subgroup
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Does not have any non-trivial normal subgroup.
And therefore, going back to our intuition that due to the fundamental theorem on homomorphisms there is one normal group per homomorphism, a simple group is one that has no non-trivial homomorphisms.
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    • How to show that a group is simple Simple group

How to show that a group is simple

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Simple group
math.stackexchange.com/questions/203168/proving-a-group-is-simple
scholarworks.sjsu.edu/cgi/viewcontent.cgi?referer=https://www.google.com/&httpsredir=1&article=5051&context=etd_theses proves that the Mathieu group M24​ is simple in just 200 pages. Nice.
Examples:
  • the alternating groups of degree 5 or greater are simple

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  • Chevalley groups An​(q)
  • Classification of finite groups
  • Cycle notation
  • PSL(2,7)
  • Quotient group
  • Semidirect product

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