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

Paediatric phantom dose study using digital radiography with variation of exposure parameters and filtration

Paediatric digital radiography remains a challenge for many radiographers. The subsequent need for focused paediatric care is outlined by ‘The Image Gently Campaign’, which reports a lack of both expertise and educational resources surrounding this area. This requirement is reinforced by The International Commission on Radiological Protection (ICRP), which identifies a need for both optimisation and consistency in digital paediatric imaging. Although a considerable proportion of recent research surrounds paediatric diagnostic imaging, Jones et. al highlights an absence of literature regarding optimisation in paediatric extremity imaging.This is of particular importance when considering paediatric patients who, due to their additional life expectancy and increased tissue radio-sensitivity, are considerably more sensitive to the detrimental effects of ionising radiation. Although the radiation dose received for diagnostic purposes is low, it is pertinent that each exposure be minimised due to the cumulative nature of radiation. The question to be addressed through our study is as follows; using a paediatric phantom with multiple bone fractures, could the variation of exposure parameters and filtration in digital radiography achieve a reduction in dose without substantially affecting image quality? This study aims to evaluate the variation of exposure parameters and filtration in image quality and dose in a paediatric phantom study using a digital radiography (DR) wireless detector.info:eu-repo/semantics/publishedVersio

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

Paediatric phantom dose optimization using digital radiography with variation of exposure parameters and filtration whilst minimising image quality impairment

Objective: To induce a reduction in dose, using a paediatric phantom, through the variation of exposure parameters and filtration, without adversely affecting image quality. Methods: All images were acquired using a Kyoto Kagaku paediatric phantom and a Canon DR detector. The phantom was positioned supine for all projections: wrist (DP, lateral) and ribs (AP, oblique). Three dose protocols were established using different mAs values (high, medium and low) and copper (Cu) filtration was added to each protocol. DAP was used to calculate the ESD for each exposure. Using ImageJ, CNR was calculated for the physical measurement of image quality. Image quality was assessed by fifteen observers (visual grading analysis (VGA)). Results: The highest doses were recorded with the high dose protocol, ranging from 5.60-39.22μGy for the wrist and 5.33-129.67μGy for the ribs. When increasing the Cu filtration a decrease in ESD was observed. A difference of 0.1 in VGA score was noted between high and low dose protocols without the use of filtration, while a difference of 0.3 was noted when using filtration. As mAs increased, VGA scores increased. Fracture visibility was minimally affected by Cu filtration or projection variation. Conclusion: The variation of exposure parameters in digital radiography can achieve a dose reduction without impairing image quality in bone fractures. Superior image quality can be achieved for DP and lateral wrist projections without Cu filtration. However, the addition of Cu filtration for the rib projections has almost no impact on overall image quality.info:eu-repo/semantics/publishedVersio

Paediatric phantom dose optimisation using digital radiography with variation of exposure parameters and filtration whilst minimising image quality impairment

Objective: To induce a reduction in dose, using a paediatric phantom, through the variation of exposure parameters and filtration, without adversely affecting image quality. Methods: All images were acquired using a Kyoto Kagaku paediatric phantom and a Canon DR detector. The phantom was positioned supine for all projections: wrist (DP, lateral) and ribs (AP, oblique). Three dose protocols were established using different mAs values (high, medium and low) and copper (Cu) filtration was added to each protocol. DAP was used to calculate the ESD for each exposure. Using ImageJ, CNR was calculated for the physical measurement of image quality. Image quality was assessed by fifteen observers (visual grading analysis (VGA)). Results: The highest doses were recorded with the high dose protocol, ranging from 5.60-39.22μGy for the wrist and 5.33-129.67μGy for the ribs. When increasing the Cu filtration a decrease in ESD was observed. A difference of 0.1 in VGA score was noted between high and low dose protocols without the use of filtration, while a difference of 0.3 was noted when using filtration. As mAs increased, VGA scores increased. Fracture visibility was minimally affected by Cu filtration or projection variation. Conclusion: The variation of exposure parameters in digital radiography can achieve a dose reduction without impairing image quality in bone fractures. Superior image quality can be achieved for DP and lateral wrist projections without Cu filtration. However, the addition of Cu filtration for the rib projections has almost no impact on overall image quality