In mathematics, especially in the field of group theory, a Carter subgroup of a finite group G is a self-normalizing subgroup of G that is nilpotent.
These subgroups were introduced by Roger Carter, and marked the beginning of the post 1960 theory of solvable groups (Wehrfritz 1999).
Vdovin (2006, 2007) showed that even if a finite group is not solvable then any two Carter subgroups are conjugate.
In the language of formations, a Sylow p-subgroup is a covering group for the formation of p-groups, a Hall π-subgroup is a covering group for the formation of π-groups, and a Carter subgroup is a covering group for the formation of nilpotent groups (Ballester-Bolinches & Ezquerro 2006, p. 100).
Together with an important generalization, Schunck classes, and an important dualization, Fischer classes, formations formed the major research themes of the late 20th century in the theory of finite soluble groups.