Symmetric group:S3: The symmetric group of degree three (order six). Also, the dihedral group of degree three (order six). See also subgroups of S3, representations of S3, and elements of S3.
Subnormal series: An ascending (resp., descending) series of subgroups with each subgroup normal in its successor (resp., predecessor).
Nilpotent implies center is normality-large (FACT): In a nilpotent group, the center intersects every nontrivial normal subgroup nontrivially.
Understanding the definition of a group (SURVEY ARTICLE): Explore the different aspects of the definition.