ON COGALOIS EXTENSIONS

[摘要] Given a number field F and a finite abelian group G congruent-to (+)i = 1t (Z/n(i)Z), n1\n2\...\n(t-1)\n(t), it is proven that there exists an extension K/F which is Galois and cogalois with Gal(K/F) congruent-to cog(K/F) congruent-to G iff the primitive n(t-1)-th roots of unity are present in F and the field obtained by adjoining the n(t)-th roots of unity to F is pure over F.

[发布日期] 1991-11-25