New documentation

1 files changed, 5 insertions, 1 deletions

diff --git a/README.md b/README.md
index 3cb4653..6e3643b 100644
--- 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.