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Additional
Hilbert class field
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Hilbert class field
In
algebraic number theory
, the
Hilbert class field
E
of a
number field
K
is the
maximal abelian
unramified
extension of
K
. Its degree over
K
equals the class number of
K
and the
Galois group
of
E
over
K
is canonically isomorphic to the
ideal class group
of
K
using
Frobenius elements
for
prime ideals
in
K
.
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