For 10 points, name these isomorphisms which map a structure to itself.
A graph is vertex transitive, if, for every pair of vertices, there exists one of these objects with a certain property. If the number of these operations for a field extension is equal to its degree, the extension is Galois. For an abelian group, every inner type of this will be trivial, as the group of the inner ones is isomorphic to the group modulo its center. A subgroup is characteristic if every one of these operations for the group maps the subgroup to itself. For a finite vector space, the group of these is the general linear group. For the complex numbers considered as a field, there are uncountably many highly-discontinuous (*) "wild" ones, but complex conjugation is the only non-trivial continuous example. No non-trivial examples of these exist for the reals or the rationals. For the Riemann sphere, the only examples of these are MÃ¶bius transformations. For finite sets, these operations are permutations of the set. For 10 points, name these isomorphisms which map a structure to itself.
A graph is vertex transitive, if, for every pair of vertices, there exists one of these objects with a certain property.
automorphisms [prompt on "isomorphism;" prompt on "homomorphism;" prompt on "endomorphism"]