From e3c7bc8c22469471654e80718c5008a525c57294 Mon Sep 17 00:00:00 2001 From: Sebastiano Tronto Date: Fri, 20 Sep 2019 11:53:44 +0200 Subject: New documentation --- README.md | 6 +++++- 1 file changed, 5 insertions(+), 1 deletion(-) 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. -- cgit v1.3