Class field towers of imaginary quadratic fields |
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Authors: | James R Brink Robert Gold |
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Institution: | (1) Battelle Columbus Laboratories, 43201 Columbus, Ohio, USA;(2) Department of Mathematics, The Ohio State University, 231 West 18th Avenue, 43210 Columbus, Ohio, USA |
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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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