Simple Group
A group is simple when its only normal subgroups are the trivial subgroup and the whole group.
Definition 7.9 (Simple Group)
A group is simple if the only normal subgroups are and itself. Thus every homomorphism is either trivial or injective. [Since , so either or .]
Example
For a prime , the cyclic group is simple.
Related
Stated in
- Definition 7.9 (Simple Group)§7.3 The Isomorphism Theorem