Faster class group computations using norm relations
Denominators of norm relations
Can we control the denominator d ?
Theorem (BFHP)
If G admits a norm relation using certain subgroups, then it also
admits one with d dividing |G|3 and using the same subgroups.
Proof sketch : There is a representation-theoretic
interpretation of existence of a norm relation. Rewrite it in terms
of idempotents, and estimate the denominators of the
idempotents.