normal_subgroup (489B)
1 # Normal subgroup 2 3 A [subgroup] N of a [group] G is *normal* if g n g^{-1} in N for every n in N and g in G 4 5 - a bit like [ideal] but [ideal] does not make sense in a group in which you have [inverse] 6 7 Can be used to build [quotient_group] by a [congruence_relation]: the equivalence class of the [identity_element] is a normal subgroup, and the other equivalence classes are [coset] of that subgroup 8 9 When the group is [abelian_group], all subgroups are normal 10 11 Up: [finite_simple_group]