Editing Core (group theory) (section)

===Definition===
For a group ''G'', the '''normal core''' or '''normal interior'''<ref>Robinson (1996) p.16</ref> of a subgroup ''H'' is the largest [[normal subgroup]] of ''G'' that is contained in ''H'' (or equivalently, the [[intersection (set theory)|intersection]] of the [[conjugate (group theory)|conjugates]] of ''H''). More generally, the core of ''H'' with respect to a [[subset]] ''S''&nbsp;&sube;&thinsp;''G'' is the intersection of the conjugates of ''H'' under ''S'', i.e.
:<math>\mathrm{Core}_S(H) := \bigcap_{s \in S}{s^{-1}Hs}.</math>

Under this more general definition, the normal core is the core with respect to ''S''&nbsp;=&thinsp;''G''. The normal core of any normal subgroup is the subgroup itself.

Dual to the concept of normal core is that of {{em|[[Normal closure (group theory)|normal closure]]}} which is the smallest normal subgroup of ''G'' containing ''H''.