JP Journal of Algebra, Number Theory and Applications
Volume 3, Issue 2, Pages 269 - 276
(August 2003)
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A
NOTE ON IMAGINARY QUADRATIC NUMBER FIELDS WITH Ck, 2 @ (4, 4)
Elliot Benjamin (U. S. A.)
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Abstract: Let
k be an imaginary quadratic number
field such that
the 2-class group of k, is of type (4,
4). We give criteria to completely determine
when
where
is the genus class field of k. We
utilize this lower bound as a first step in
finding fields k such that
has
which we demonstrate implies that rank
where is
the Hilbert 2-class field of k. The
determination of fields k with rank
is a crucial element in making progress on the
open question of which algebraic number fields
k have infinite 2-class field tower. |
Keywords and phrases: genus class field, Hilbert 2-class field,
unit index, class number formula, imaginary quadratic
number field, 2-class field tower. |
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