# Centrally closed subgroup

- 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.

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