The Artin Symbol as Canonic Capitulation Map. Draft
نویسنده
چکیده
We show that there is a canonical, order preserving map ψ of lattices of subgroups, which maps the lattice Sub(A) of subgroups of the ideal class group of a galois number field K into the lattice Sub(H/K) of subfields of the Hilbert class field. Furthermore, this map is a capitulation map in the sense that all the primes in the classes of A ⊂ A capitulate in ψ(A). In particular we have a new, strong version of the generalized Hilbert 94 Theorem, which confirms the result of Myiake and adds more structure to (part) of the capitulation kernel of subfields of H
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