A Stabilizer

1. Any person or thing that brings stability.
2. Any substance added to something in order to stabilize it.
3. A gyroscopically controlled fin or similar device that prevents the excess rolling of a ship in rough seas.
4. An airfoil that stabilizes the flight of an aircraft or missile.
5. (textiles) A piece of backing fabric used in embroidery.
6. (mathematics) For a group operating on a set and an element x of the set, the set of all group elements fixing x.