Abstract
The Galois group of the maximal unramified p-extension (p 2) of an imaginary quadratic field is investigated for the case where the group is finite. It is shown that the group can be generated by not more than two generators with two relations. One of the relations can be taken from the 3rd term of the Zassenhaus filtration of the free group, and the second, from the 2nd, 5th, or 7th term.
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Literature cited
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Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 46, pp. 5–13, 1974.
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Venkov, B.B., Koch, H. The p-tower of class fields for an imaginary quadratic field. J Math Sci 9, 291–299 (1978). https://doi.org/10.1007/BF01085047
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DOI: https://doi.org/10.1007/BF01085047