Higher Degree Hilbert Symbol Equivalence of Algebraic Number Fields, II Original Research Article

Hilbert symbol equivalence of degreenbetween two global fields containing a primitiventh root of unity is an isomorphism between the groups ofnth power classes of these fields preserving Hilbert symbols of degreen. In the paper we prove that ifnis an odd prime number then two number fields are Hilbert equivalent if and only if there exists a bijection between the sets ofn-adic primes of the two fields which preserves the local degrees. This generalizes the known result forn=2.