On the Sylow graph of a finite group

The final publication is available at Springer via http://dx.doi.org/10.1007/s11856-011-0138-xLet G be a finite group and Gp be a Sylow p-subgroup of G for a prime p in pi(G), the set of all prime divisors of the order of G. The automiser Ap(G) is defined to be the group NG(Gp)/GpCG(Gp). We define the Sylow graph gamma A(G) of the group G, with set of vertices pi(G), as follows: Two vertices p, q ¿ ¿(G) form an edge of ¿A(G) if either q ¿ ¿(Ap(G)) or p ¿ ¿(Aq(G)). The following result is obtained: Theorem: Let G be a finite almost simple group. Then the graph ¿A(G) is connected and has diameter at most 5. We also show how this result can be applied to derive information on the structure of a group from the normalizers of its Sylow subgroups.The second and third authors have been supported by Proyecto MTM2007-68010-C03-03 and Proyecto MTM2010-19938-C03-02, Ministerio de Educacion y Ciencia and FEDER, Spain.Kazarin, SL.; Martínez Pastor, A.; Pérez-Ramos, M. (2011). On the Sylow graph of a finite group. Israel Journal of Mathematics. 186(1):251-271. doi:10.1007/s11856-011-0138-xS2512711861Z. Arad and D. Chillag, Finite groups containing a nilpotent Hall subgroup of even order, Houston Journal of Mathematics 7 (1981), 23–32.H. Azad, Semi-simple elements of order 3 in finite Chevalley groups, Journal of Algebra 56 (1979), 481–498.A. Ballester-Bolinches, A. Martínez-Pastor, M. C. Pedraza-Aguilera and M. D. Pérez-Ramos, On nilpotent-like fitting formations, in Groups St. Andrews 2001 in Oxford, (C. M. Campbell et al., eds.) London Mathematical Society Lecture Note Series 304, Cambridge University Press, 2003, pp. 31–38.M. Bianchi, A. Gillio Berta Mauri and P. Hauck, On finite groups with nilpotent Sylow normalizers, Archiv der Mathematik 47 (1986), 193–197.A. Borel, R. Carter, C.W. Curtis, N. Iwahori, T. A. Springer, R. Steinberg, Seminar on Algebraic Groups and Related Finite Groups, Lecture Notes of Mathematics 131 Springer, Berlin, 1970.N. Bourbaki, Éléments de mathématique: Groupes et algèbres de Lie, Chapters IV, V, VI, Hermann, Paris, 1968.R. W. Carter, Simple groups of Lie type, Wiley, London, 1972.R. W. Carter, Conjugacy classes in the Weyl group, Compositio Mathematica 25 (1972), 1–59.R. W. Carter, Finite Groups of Lie Type: Conjugacy Classes and Complex Characters, Wiley, London, 1985.A. D’Aniello, C. De Vivo and G. Giordano, On certain saturated formations of finite groups, in Proceedings Ischia Group Theory 2006, (T. Hawkes, P. Longobardy and M. Maj, eds.) World Scientific, Hackensack, NJ, 2007, pp. 22–32.A. D’Aniello, C. De Vivo and G. Giordano, Lattice formations and Sylow normalizers: a conjecture, Atti del Seminario Matematico e Fisico dell’ Università di Modena e Reggio Emilia 55 (2007), 107–112.A. D’Aniello, C. De Vivo, G. Giordano and M. D. Pérez-Ramos, Saturated formations closed under Sylow normalizers, Communications in Algebra 33 (2005), 2801–2808.K. Doerk, T. Hawkes, Finite soluble groups, Walter De Gruyter, Berlin-New York, 1992.G. Glauberman, Prime-power factor groups of finite groups II, Mathematische Zeitschrift 117 (1970), 46–56.D. Gorenstein, R. Lyons, The local 2-structure of groups of characteristic 2 type, Memoirs of the American Mathematical Society 42, No. 276, Providence, RI, 1983.R. M. Guralnick, G. Malle and G. Navarro, Self-normalizing Sylow subgroups, Proceedings of the American Mathematical Society 132 (2004), 973–979.F. Menegazzo, M. C. Tamburini, A property of Sylow p-normalizers in simple groups, Quaderni del seminario Matematico di Brescia, n. 45/02 (2002).R. Steinberg, Lectures on Chevalley Groups, Yale University, New Haven, Conn., 1968.E. Stensholt, An application of Steinberg’s construction of twisted groups, Pacific Journal of Mathematics 55 (1974), 595–618.E. Stensholt, Certain embeddings among finite groups of Lie type, Journal of Algebra 53 (1978), 136–187.K. Zsigmondy, Zur Theorie der Potenzreste, Monatshefte für Mathematik and Physik 3 (1892), 265–284

OPTIMAX 2017 : radiation dose, image quality optimisation,the use of new technology in medical imaging

This year OPTIMAX settled in Oslo. After the successof previous years, we are proud to present the fourthEbook. As in previous years, the group was madeup of PhD-, MSc- and BSc students as well astutors from the seven European partner universities.Professional mix was drawn from medical physics/physics and radiography. OPTIMAX 2017 was partlyfunded by the partner universities and partly by theparticipants. Two students from South Africa and twofrom Brazil were invited by Hanze UAS (Groningen)and ESTeSL (Lisbon) summer school includedlectures and group projects in which experimentalresearch was conducted in four teams. Four research projects were performed with a focuson radiation dose optimization and image quality,namely: Possible dose reduction for pediatric patientsfor conventional radiology; Can the tube voltage belowered with the use of direct-conversion flat paneldetector system?; Impact of body size and kV in chestradiography; Quantity assessment on Image quality ofCBCT images of head phantom with implants of metaland ceramic objects.The last day of OPTIMAX 2017there was a poster session and a conference, in whichthe research teams presented their posters and oralpresentations. This book comprises of two sections, the first twochapters concern generic background informationabout international teamwork during the OPTIMAXsummerschool. The next chapters with theory on which the researchprojects were built. The second section containsthe research papers of the four research projects.Two research papers, Can the tube voltage belowered with the use of direct-conversion flat-paneldetector system? And Impact of body size and kV inchest radiography: Experimental receiver operatingcharacteristic analysis using a Multipurpose ChestPhantom “Lungman” have been accepted for the ECRconference, Vienna, 2018 as oral presentations

Filtration Properties of Ferric Hydroxide Precipitate in Nickel Production

Ferric iron removal from the nickel electrolyte at Glencore Nikkelverk AS in Kristiansand, Norway, is achieved by precipitation of iron hydroxide followed by filtration, and it is desirable to improve filtration properties of the precipitated iron hydroxide in order to decrease the filtration time. The effect of increasing the residence time from the current 45 min to 75 min and temperature from 65 °C to 90 °C on the filtration properties of the precipitated iron hydroxide (akaganéite) was studied by simulating the industrial process conditions in a continuous reactor setup operating at steady state, using ferrous-containing process solution as feed material. It was possible to decrease the filter cake resistance by both increasing residence time and temperature, but temperature gave the most pronounced effect and reduced the filter cake resistance by one order of magnitude

Which Scoring Rule Maximizes Condorcet Efficiency Under Iac?

Consider an election in which each of the n voters casts a vote consisting of a strict preference ranking of the three candidates A, B, and C. In the limit as n→∞, which scoring rule maximizes, under the assumption of Impartial Anonymous Culture (uniform probability distribution over profiles), the probability that the Condorcet candidate wins the election, given that a Condorcet candidate exists? We produce an analytic solution, which is not the Borda Count. Our result agrees with recent numerical results from two independent studies, and contradicts a published result of Van Newenhizen (Economic Theory 2, 69–83. (1992)). Copyright Springer 2005Condorcet efficiency, scoring systems, Borda count, impartial anonymous culture, voting, C67,