Faster class group computations using norm relations
Norm relations
Definition : norm relation with denominator d
d =
X
i
aiNHi
bi
with ai, bi ∈ Z[G] and d ∈ Z>0.
For all x ∈ K×, we have
xd
=
Y
i
NK/KHi (xbi
)

ai
,
so xd belongs to the subgroup generated by the subfields.
The S-units from the subfields generate a Z[G]-submodule of
finite index in the S-units of K.