Faster class group computations using norm relations
Existence of norm relations
When do such relations exist?
Theorem (BFHP, Wolf)
A finite group G admits a norm relation if and only if G contains
I a non-cyclic subgroup of order pq (p,q, primes not
necessarily distinct), or
I a subgroup isomorphic to SL2(Fp) where p = 22k
+ 1 is a
Fermat prime with k > 1.
Also : criterion to test existence with specific subgroups, more
precise information in the abelian case.