Simple group

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 11

 Ancestors (8)

Normal subgroup
Quotient group
Subgroup
Group
Algebra
Area of mathematics
Mathematics
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 Incoming links (6)

Chevalley groups $A_{n} (q)$
Classification of finite groups
Cycle notation
PSL(2,7)
Quotient group
Semidirect product