Recent examples of periodic bifurcations in
descendant trees of finite p-groups with
?are used to show that
the possible p-class tower groups G of certain multiquadratic fields K with p- class
group of type (2,2,2), resp. (3,3), form periodic sequences in the descendant tree of the
elementary Abelian root
[1] | Mayer, D.C. (2015) Periodic Bifurcations in Descendant Trees of Finite p-Groups. Advances in Pure Mathematics, 5, 162-195. http://dx.doi.org/10.4236/apm.2015.54020 Special Issue on Group Theory, March 2015. (arXiv: 1502.03390v1 [math.GT] 11 Feb 2015.)
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[2] | Mayer, D.C. (2015) Index-p Abelianization data of p-Class Tower Groups, to appear in Advances in Pure Mathematics, 5, Special Issue on Number Theory and Cryptography, April 2015. (arXiv: 1502.03388v1 [math.NT] 11 Feb 2015.)
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[7] | Gamble, G., Nickel, W. and O’Brien, E.A. (2006) ANU p-Quotient—p-Quotient and p-Group Generation Algorithms. An accepted GAP 4 package, available also in MAGMA.
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[8] | The GAP Group (2015) GAP—Groups, Algorithms, and Programming—a System for Computational Discrete Algebra. Version 4.7.7, Aachen, Braunschweig, Fort Collins, St. Andrews. http://www.gap-system.org
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[11] | The MAGMA Group (2015) MAGMA Computational Algebra System. Version 2.21-2, Sydney.
http://magma.maths.usyd.edu.au
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[12] | Bush, M.R. and Mayer, D.C. (2015) 3-Class Field Towers of Exact Length 3. J. Number Theory, 147, 766-777. (arXiv: 1312.0251v1 [math.NT] 1 Dec 2013.)
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[13] | Hilbert, D. (1894) Ueber den Di-richlet'schen biquadratischen Zahlk?rper. Mathematische Annalen, 45, 309-340.
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[14] | Azizi, A., Zekhnini, A. and Taous, M. (2015) Coclass of for Some Fields with 2-Class Groups of Type . To appear in J. Algebra Appl.
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[16] | Mayer, D.C. (2013) The Distribution of Second p-Class Groups on Coclass Graphs. J. Théor. Nombres Bordeaux, 25, 401-456. (27th Journées Arithmétiques, Faculty of Mathematics and In-formatics, Univ. of Vilnius, Lithuania, 2011.)
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[17] | Mayer, D.C. (2012) The Second p-Class Group of a Number Field. Int. J. Number Theory, 8, 471-505.
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[18] | Mayer, D.C. (2014) Principalization Algorithm via Class Group Structure. J. Théor. Nombres Bordeaux, 26, 415-464.
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[19] | Boston, N., Bush, M.R. and Hajir, F. (2015) Heuristics for p-Class Towers of Imaginary Quadratic Fields. To appear in Math. Annalen. (arXiv: 1111.4679v2 [math.NT] 10 Dec 2014.)
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