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Remarks concerning the 2-Hilbert class field of imaginary quadratic number fields

Published online by Cambridge University Press:  17 April 2009

Elliot Benjamin
Elliot Benjamin
Affiliation:
Mathematics Department, Unity College, Unity ME 04988-9502, United States of America
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Let k be an imaginary quadratic number field and let k1 be the 2-Hilbert class field of k. If Ck,2, the 2-Sylow subgroup of the ideal class group of k, is elementary and |Ck,2|≥ 8, we show that Ck1,2 is not cyclic. If Ck,2 is isomorphic to Z/2Z × Z/4Z and Ck1,2 is elementary we show that k has finite 2-class field tower of length at most 2.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 48 , Issue 3 , December 1993 , pp. 379 - 383
Copyright
Copyright © Australian Mathematical Society 1993

References

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