Gaschütz group

Definition
A Gaschütz group is a group with the property that every subgroup in it is c-closed: in other words, every subgroup occurs as the centralizer of some subgroup.

Formalisms
The property of being a Gaschütz group can be thought of as the following two subgroup properties collapsing to the same thing in the group:

Any subgroup = c-closed subgroup

The Hamiltonian operator takes a subgroup property and outputs the property of being a group in which every subgroup has the property. The property of being Gaschütz is obtained by applying the Hamiltonian operator to the subgroup property of being c-closed.

Weaker properties

 * Centerless group