... (We can ignore what happens to the identity since the identity is fixed for all automorphisms, ) In other ...Automorphisms must preserve the order of an element. ...
... If are automorphisms such that , then it is clear that (since any element of is of the form ). ... The group of automorphisms of a finite cyclic group is studied. ...
... Indeed, the automorphisms of K which leave Q fixed are given below by the values on the basis { 1, sqrt 2, sqrt 3, sqrt 6} for K/Q: 1, the identity,. ...
... K / Q ) is isomorphic to a dihedral group: a group of order 4 generated by two elements of order 2. These two elements correspond to the automorphisms: ϕ : ia ...
... 1. Let E be an extension field of F. As discussed in class, let G = Aut[F]E = {automorphisms of E that fix F}. If t is an element of G, show that E^t = {x ...
