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New number fields with known p-class tower


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[1] ARTIN, E.: Beweis des allgemeinen Reziprozitätsgesetzes, Abh. Math. Sem. Univ. Hamburg 5 (1927), 353-363.10.1007/BF02952531Search in Google Scholar

[2] ARTIN, E.: Idealklassen in Oberkörpern und allgemeines Reziprozitätsgesetz, Abh. Math. Sem. Univ. Hamburg 7 (1929), 46-51.10.1007/BF02941159Search in Google Scholar

[3] ASCIONE, J. A.: On 3-groups of second maximal class. Ph.D. Thesis, Austral. National Univ., Canberra, 1979.10.1017/S0004972700006298Search in Google Scholar

[4] AZIZI, A.-ZEKHNINI, A.-TAOUS, M.: Coclass of Gal_k(2)2|k) for some fieldsk = Q(√p1p2q, √−1) with 2-class groups of type (2, 2, 2), J. Algebra Appl., 2015 (to appear).Search in Google Scholar

[5] BARTHOLDI, L.- BUSH, M. R.: Maximal unramified 3-extensions of imaginary quadratic fields and SL2Z3, J. Number Theory 124 (2007), 159-166.10.1016/j.jnt.2006.08.008Search in Google Scholar

[6] BESCHE, H. U.-EICK, B.-O’BRIEN, E. A.: A millennium project: constructing small groups, Int. J. Algebra Comput. 12 (2002), 623-644.10.1142/S0218196702001115Search in Google Scholar

[7] BESCHE, H. U.-EICK, B.-O’BRIEN, E. A.: The SmallGroups Library - a Library of Groups of Small Order, 2005, an accepted and refereed GAP package, available also in MAGMA.Search in Google Scholar

[8] BOSMA, W.-CANNON, J.-PLAYOUST, C.: The Magma algebra system. I. The user language, J. Symbolic Comput. 24 (1997), 235-265.10.1006/jsco.1996.0125Search in Google Scholar

[9] BOSMA, W.-CANNON, J. J.-FIEKER, C.-STEELS, A. (EDS.): Handbook of Magma functions. Edition 2.21, Univ. of Sydney, Sydney, 2015.Search in Google Scholar

[10] BOSTON, N.-BUSH, M. R.-HAJIR, F.: Heuristics for p-class towers of imaginary quadratic fields, Math. Annalen, 2015 (to appear); arXiv: 1111.4679v2 [math.NT] 10 Dec., 2014.Search in Google Scholar

[11] BUSH, M. R.-MAYER, D. C.: 3-class field towers of exact length 3, J. Number Theory 147 (2015), 766-777.10.1016/j.jnt.2014.08.010Search in Google Scholar

[12] CHANG, S. M.-FOOTE, R.: Capitulation in class field extensions of type (p, p), Can. J. Math. 32 (1980), 1229-1243.10.4153/CJM-1980-091-9Search in Google Scholar

[13] GOLOD, E. S.-SHAFAREVICH, I. R.: On class field towers, Izv. Akad. Nauk SSSR, Ser. Mat. 28 (1964), no. 2, 261-272 (In Russian); English transl. in Amer. Math. Soc. Transl. (2) 48 (1965), 91-102.Search in Google Scholar

[14] KOCH, H.-VENKOV, B. B.: Über den p-Klassenkörperturm eines imaginär-quadratischen Zahlkörpers, Astérisque 24-25 (1975), 57-67.Search in Google Scholar

[15] The MAGMA Group, MAGMA Computational Algebra System, Version 2.21-8, Sydney, 2015, http://magma.maths.usyd.edu.auSearch in Google Scholar

[16] MAYER, D. C.: The second p-class group of a number field, Int. J. Number Theory 8 (2012), 471-505.10.1142/S179304211250025XSearch in Google Scholar

[17] MAYER, D. C.: Transfers of metabelian p-groups, Monatsh. Math. 166 (2012), 467-495.10.1007/s00605-010-0277-xSearch in Google Scholar

[18] MAYER, D. C.: Principalization algorithm via class group structure, J. Théor. Nombres Bordeaux 26 (2014), 415-464.10.5802/jtnb.874Search in Google Scholar

[19] MAYER, D. C.: The distribution of second p-class groups on coclass graphs, J. Théor. Nombres Bordeaux 25 (2013), no. 2, 401-456; 27th Journées Arithmétiques, Faculty of Math. and Inform., University of Vilnius, Lithuania, 2011.Search in Google Scholar

[20] MAYER, D. C.: Periodic bifurcations in descendant trees of finite p-groups, Adv. Pure Math. 5 (2015), 162-195.10.4236/apm.2015.54020Search in Google Scholar

[21] MAYER, D. C.: Index-p abelianization data of p-class tower groups, Adv. Pure Math. 5 (2015), 286-313; 29th Journées Arithmétiques, Univ. of Debrecen, Hungary, 2015.Search in Google Scholar

[22] MAYER, D. C.: Periodic sequences of p-class tower groups, in: 1st Internat. Conference on Groups and Algebras-ICGA ’15, Shanghai, China, 2015, J. Appl. Math. Phys. 3 (2015), 746-756.10.4236/jamp.2015.37090Search in Google Scholar

[23] NEBELUNG, B.: Klassifikation metabelscher 3-Gruppen mit Faktorkommutatorgruppe vom Typ (3, 3) und Anwendung auf das Kapitulationsproblem. Inauguraldissertation, Universität zu Köln, 1989.Search in Google Scholar

[24] NEWMAN, M. F.: Determination of groups of prime-power order, in: Proc. Miniconf. Canberra, Group Theory, 1975, Lecture Notes in Math., Vol. 573, Springer, Berlin, 1977, pp. 73-84.10.1007/BFb0087814Search in Google Scholar

[25] O’BRIEN, E. A.: The p-group generation algorithm, J. Symbolic Comput. 9 (1990), 677-698.10.1016/S0747-7171(08)80082-XSearch in Google Scholar

[26] THE PARI GROUP, PARI/GP, Version 2.7.5, Bordeaux, 2015, http://pari.math.u-bordeaux.frSearch in Google Scholar

[27] SCHOLZ, A.-TAUSSKY, O.: Die Hauptideale der kubischen Klassenkörper imagin är quadratischer Zahlkörper: ihre rechnerische Bestimmung und ihr Einfluß auf den Klassenkörperturm, J. Reine Angew.Math. 171 (1934), 19-41.Search in Google Scholar

[28] SHAFAREVICH, I. R.: Extensions with prescribed ramification points, Publ. Math., Inst. Hautes Études Sci. 18 (1964), 71-95, (In Russian); English transl. Amer. Math. Soc. Transl., II. Ser., 59 (1966), 128-149. Search in Google Scholar

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