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

Part of: Algebraic number theory: global fields

Published online by Cambridge University Press:  28 September 2015

ELLIOT BENJAMIN  and
C. SNYDER
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]
*
✉[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.

Keywords

quadratic number fieldideal class groupnarrow class group

MSC classification

Primary: 11R11: Quadratic extensions
Secondary: 11R29: Class numbers, class groups, discriminants
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 100 , Issue 1 , February 2016 , pp. 21 - 32
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

References

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Lemmermeyer, F., ‘Relations in the 2-class group of quadratic number fields’, J. Aust. Math. Soc. 93 (2012), 115–120.CrossRefGoogle Scholar