JP Journal of Algebra, Number Theory and Applications
Volume 5, Issue 1, Pages 173 - 195
(April 2005)
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IMAGINARY BICYCLIC BIQUADRATIC FIELDS WITH ELEMENTARY 2-CLASS GROUP
Thomas M. Mccall (U. S. A.) and Charles J. Parry (U. S. A.)
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Abstract: In this article we classify all imaginary bicyclic biquadratic fields which have an elementary 2-class group provided the discriminant of the real quadratic subfield has no prime divisors congruent to 3 modulo 4. A necessary condition for a biquadratic field to have elementary 2-class group is that no quadratic subfield have a cyclic factor of order greater than 4 in its 2-class group. However, when this condition is satisfied, it is shown that every abelian group of exponent 2 or 4 occurs as a 2-class group of some biquadratic field. |
Keywords and phrases: elementary 2-class group, imaginary bicyclic biquadratic fields. |
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