Equality of norm groups of subextensions of Sn(n ≤ 5) extensions of algebraic number fields

[摘要] Let E/k be a Galois extension of algebraic number fields with the Galois group isomorphic to the symmetric group S-n on n less than or equal to 5 letters. For any field extensions k subset of or equal to K, L subset of or equal to E a necessary and a sufficient condition is given for the equality NK/kK* = NL/kL* to hold, where NK/kK* is the group of norms from K to k of the elements of the multiplicative group K* of K. (C) 2003 Elsevier Inc. All rights reserved.

[发布日期] 2003-10-01