Abstract
In their 1934 paper, Scholz and Taussky defined the notion of capitulation type for imaginary quadratic fields whose ideal class group has a Sylow 3-subgroup which is elementary abelian of order 32. For one particular capitulation type (type D) they prove that the 3-class field tower of the quadratic field has length 2. They briefly indicate how a similar result can be shown to hold for capitulation type E. In this paper we give a simpler proof of their type D result and we construct a group theoretic counterexample to their type E assertion.
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References
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Brink, J.R., Gold, R. Class field towers of imaginary quadratic fields. Manuscripta Math 57, 425–450 (1987). https://doi.org/10.1007/BF01168670
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DOI: https://doi.org/10.1007/BF01168670