commit e3c7bc8c22469471654e80718c5008a525c57294
parent b32aefa354eb4cff9447d4de9cd25ebd424721fa
Author: Sebastiano Tronto <sebastiano.tronto@gmail.com>
Date: Fri, 20 Sep 2019 11:53:44 +0200
New documentation
Diffstat:
1 file changed, 5 insertions(+), 1 deletion(-)
diff --git a/README.md b/README.md
@@ -9,10 +9,14 @@ A Kummer Extension of Q is a field extension of the form Q_{M,N}:=
Q(\zeta_M,G^{1/N}), where:
* M and N are integers with N dividing M;
* \zeta_M is a root of unity of order M;
-* G is a finitely generated subgroup of the multiplicative group of Q;
+* G is a finitely generated subgroup of the multiplicative group Q* of Q;
* G^{1/N} is the set of all elements x of an algebraic closure of Q such that
x^n belongs to G.
+In other words, it is a number field generated by finitely many elements of
+the form a^{1/n} and "at least sufficiently many" roots of unity to make
+this field Galois over Q.
+
The main importance of this script is to show that, for a fixed group G as
above, one can compute in a finite time a finite-case-distinction formula
that computes the degrees [Q_{M,N}:Q] of such extensions when M and N vary.
