Centrally-closed subgroup

In mathematics, in the realm of group theory, a subgroup of a group is said to be centrally closed if the centralizer of any nonidentity element of the subgroup lies inside the subgroup.

Some facts about centrally closed subgroups:

• Every malnormal subgroup is centrally closed.
• Every Frobenius kernel is centrally closed.
• SA subgroups are precisely the centrally closed Abelian subgroups.
• The trivial subgroup and the whole group are centrally closed.