It is in the field of abstract algebra. Sorry that I couldn't provide more information. Serge Lang, Algebra, Graduate texts in mathematics vol.211 could be useful. Thank you.

= Problem 17.21 (10). Let H = (o) be the group generated by an element O E Auto(Q) and k OH the fixed field of H. Prove that every finite extension K/k is cyclic. (|H| may be infinite. But you do not need infinite Galois theory) = Problem 17.21 (10). Let H = (o) be the group generated by an element O E Auto(Q) and k OH the fixed field of H. Prove that every finite extension K/k is cyclic. (|H| may be infinite. But you do not need infinite Galois theory)