On the computation of quadratic $2$-class groups

If a number field F contains the 2`-th roots of unity then the wild kernel of F and its logarithmic `-class group have the

In the following, we will refer to the base case as the strategy consisting of finding the relation matrix without using the large prime variants or the smoothness batch test,

Besides this, in general it is not known which of the local but not global isomorphic covering groups is the invariance group; for instance, it is hard to say

This procedure should work for any higher class group of totally real abelian number fields, but in cases different from real quadratic fields the group theory which is necessary

Thus each mathematical symbol (G, L,. .) has a single definite meaning inside each exercise, but might have different meanings from an exercise to another.. It is not required to

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During the writing of this article, we have been informed of papers by Wang [41, Theorem 1.1] (dealing with the non-trivial case ℓ 6 = p and men- tioning, without proofs, the