Editing Group (mathematics) (section)

=== Simple groups ===
When a group <math>G</math> has a normal subgroup <math>N</math> other than <math>\{1\}</math> and <math>G</math> itself, questions about <math>G</math> can sometimes be reduced to questions about <math>N</math> and {{tmath|1= G/N }}. A nontrivial group is called ''[[simple group|simple]]'' if it has no such normal subgroup. Finite simple groups are to finite groups as prime numbers are to positive integers: they serve as building blocks, in a sense made precise by the [[Jordan–Hölder theorem]].