Topic summary
Decomposition group
Extracted from the Wikipedia article Splitting of prime ideals in Galois extensions.
Primes p ≡ 1 mod 4
The decomposition groups in this case are both the trivial group {1}; indeed the automorphism σ switches the two primes (2 + 3i) and (2 − 3i), so it cannot be in the decomposition group of either prime. The inertia group, being a subgroup of the decomposition group, is also the trivial group. There are two residue fields, one for each prime,