We call a (q - 1)-th Kummer extension of a cyclotomic function field a quasi-cyclotomic function field if it is Galois, but non-abelian, over the rational function field with the constant field of q elements. In this paper, we determine the structure of the Galois groups of a kind of quasi-cyclotomic function fields over the base field. We also give the genus formulae of them.
|Number of pages||8|
|Journal||Journal of Number Theory|
|Publication status||Published - Nov 2012|
- cyclotomic function field
- galois group
- quasi-cyclotomic function field