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| P26008-N25 | |
Towers of p-class fields over algebraic number fields |
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Cooperations 1.BUSH, Michael R., Prof., Ph.D. Washington and Lee University, Department of Mathematics, Robinson Hall 4 Lexington, VA 24450 (Virginia), USA bushm@wlu.edu http://home.wlu.edu/~bushm/ An unexpected and particularly fruitful cooperation resulted from my meeting with Nigel Boston, Michael R. Bush, and Farshid Hajir at the Workshop on Golod-Shafarevich groups and algebras and rank gradient, organized by the Erwin Schrödinger Institute, Vienna, in August 2012. We solved the uncertainty about the exact length of the 3-tower over complex quadratic fields with transfer kernel types in section E, which had been raised by Brink and Gold's doubts about a claim of Scholz and Taussky. Together with Michael R. Bush, I started a cooperation concerning the length of 3-towers, based on the concept of Schur σ-groups. 2. NEWMAN, Mike F., Prof., Ph.D. The Australian National University, Centre for Mathematics and its Applications Canberra, ACT 0200 (Australian Capital Territory), New South Wales, Australia mike.newman@maths.anu.edu.au newman2603@gmail.com http://maths.anu.edu.au/about-us/people/michael-newman Initiated by Judith Ascione, I am in continuous contact with Mike F. Newman since October 2010. He gives me valuable suggestions concerning the use of the SmallGroups library and ANUPQ package of GAP and MAGMA, and precious aid in identifying finite metabelian p-groups, produced by various approaches to the classification problem, in particular, by Bagnera, Schreier, P. Hall, Easterfield, Blackburn, Miech, James, Ascione, and Nebelung. Recently we started a collaboration devoted to p-groups which arise as p-tower groups of quadratic fields. The groups are either metabelian for p ≥ 5, connected with Hall's isoclinism family Φ6, or non-metabelian for p = 3, arising from Scholz and Taussky's sections E to H of transfer kernel types. 3. KISHI, Yasuhiro, Prof., Ph.D. Aichi University of Education Nagoya, Japan ykishi@auecc.aichi-edu.ac.jp Initiated by the supervisor of his Ph.D. Thesis, Katsuya Miyake, and starting with our personal acquaintance at the 29ièmes Journées Arithmétiques 2015 in Debrecen, we are working on cyclic quartic fields Q(d1/2(ζ - ζ-1)), ζ = exp(2π i/5), containing 51/2, based on the Quintic Reflection Theorem by Kishi. 4. The Research Group in Morocco: AZIZI, Abdelmalek, Prof., Ph.D. Université Mohammed Premier, Faculté des Sciences d'Oujda (FSO), Boulevard Mohammed 6 60000 Oujda, Maroc abdelmalekazizi@yahoo.fr http://www.academie.hassan2.sciences.ma/es/cv/cv.php?nom1=AZIZI AYADI, Mohammed, Prof., Ph.D. Université Mohammed Premier, Faculté des Sciences d'Oujda (FSO), Boulevard Mohammed 6 60000 Oujda, Maroc mohammed.idaya93@gmail.com ISMAÏLI, Moulay Chrif, Prof., Ph.D. Université Mohammed Premier, Faculté des Sciences d'Oujda (FSO), Boulevard Mohammed 6 60000 Oujda, Maroc mcismaili@yahoo.fr DERHEM, Aïssa, Ph.D. 4 Rue Blida 20100 Casablanca, Maroc aderhem@usa.net TALBI, Mohamed, Prof., Ph.D. Université Mohammed Premier, Faculté des Sciences d'Oujda (FSO), Boulevard Mohammed 6 60000 Oujda, Maroc ksirat1971@gmail.com TALBI, Mohammed, Ph.D. Université Mohammed Premier, Faculté des Sciences d'Oujda (FSO), Boulevard Mohammed 6 60000 Oujda, Maroc talbimm@gmail.com ZEKHNINI, Abdelkader, Prof., Ph.D. Université Mohammed Premier, Faculté des Sciences d'Oujda (FSO), Boulevard Mohammed 6 60000 Oujda, Maroc zekha1@yahoo.fr TAOUS, Mohammed, Prof., Ph.D. Université Moulay Ismaïl, Faculté des Sciences et Techniques (FST) 57000 Errachidia, Maroc taousm@hotmail.com Since December 2001, I am in contact with Abdelmalek Azizi and his research group, initiated by Aïssa Derhem in Casablanca, Morocco. The research group consists of Mohammed Ayadi, Moulay Chrif Ismaïli, and Mohamed Talbi at the Faculté des Sciences d' Oujda (FSO), and Mohammed Taous at the Faculté des Sciences et Technologie (FST), Errachidia. Together with Azizi's former Ph.D. dissertants Mohammed Talbi and Abdelkader Zekhnini, we are conducting our joint investigations of bicyclic biquadratic fields Q(ζ,d1/2) containing either the fourth (n = 4) or the third (n = 3) primitive root of unity ζ = exp(2π i/n) and cyclic quartic fields Q(d1/2(ζ - ζ-1)), ζ = exp(2π i/5), containing 51/2. The work is based on recent preparations. |
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With support from |
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