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ELEMENTS OF ORDER FOUR IN THE NARROW CLASS GROUP OF REAL QUADRATIC FIELDS

Published online by Cambridge University Press:  28 September 2015

ELLIOT BENJAMIN*
Affiliation:
Department of Mathematics and Statistics, University of Maine, Orono, ME 04469, USA email [email protected]
C. SNYDER
Affiliation:
Department of Mathematics and Statistics, University of Maine, Orono, ME 04469, USA email [email protected]
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Abstract

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Using the elements of order four in the narrow ideal class group, we construct generators of the maximal elementary $2$-class group of real quadratic number fields with even discriminant which is a sum of two squares and with fundamental unit of positive norm. We then give a characterization of when two of these generators are equal in the narrow sense in terms of norms of Gaussian integers.

Type
Research Article
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

References

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