The set of all automorphisms of an object forms a group, called the automorphism group. Algebraic varieties differ widely in how many birational automorphisms they have. The Cremona group, the group of birational automorphisms of the plane, is generated by blowups. Note that automatically "G" acts by automorphisms (bijections) on the set. This number is maximal by virtue of Hurwitz's theorem on automorphisms . Almost all planar graphs have an exponential number of automorphisms. In this case the theory of automorphisms of a finite cyclic group can be used. Another important question is the existence of automorphisms in recursion-theoretic structures. A curve is stable if it has only a finite group of automorphisms. It is the Lie algebra of the group of automorphisms of . These 7 maximal orders are all equivalent under automorphisms. For example, all order automorphisms of a power set are induced by permutations of . Note that, computing symmetry-breaking conditions requires finding all automorphisms of a given query graph. Dualities can be viewed in the context of the Heawood graph as color reversing automorphisms. The other automorphisms are called outer automorphisms.