Normal subgroups and class sizes of elements of prime power order

[EN] If G is a finite group and N is a normal subgroup of G with two C-conjugacy class sizes of elements of prime power order, then we show that N is nilpotent.We would like to thank the referee for some simplifications in the original proofs. This research was supported by the Spanish Government, Proyecto MTM2010-19938-C03-02, and by the Valencian Government, Proyecto PROMETEO/2011/30. The first author was also supported by grant Fundacio Caixa-Castello P11B2010-47.Beltrán, A.; Felipe Román, MJ. (2012). Normal subgroups and class sizes of elements of prime power order. Proceedings of the American Mathematical Society. 140(12):4105-4109. https://doi.org/10.1090/S0002-9939-2012-11276-6S410541091401

Multiplying a conjugacy class by its inverse in a finite group

[EN] Suppose that G is a finite group and K is a non-trivial conjugacy class of G such that KK (-1) = 1 a D a D (-1) with D a conjugacy class of G. We prove that G is not a non-abelian simple group and we give arithmetical conditions on the class sizes determining the solvability and the structure of aOE (c) K > and aOE (c) D >.The authors gratefully acknowledge all helpful comments made by the referee. The results in this paper are part of the third author's Ph.D. thesis, and she acknowledges the predoctoral grant PRE-DOC/2015/46, Universitat Jaume I. The first and second authors are supported by the Valencian Government, Proyecto PROMETEOII/2015/011. The first and third authors are also partially supported by Universitat Jaume I, grant P11B2015-77.Beltrán, A.; Felipe Román, MJ.; Melchor, C. (2018). Multiplying a conjugacy class by its inverse in a finite group. Israel Journal of Mathematics. 227(2):811-825. https://doi.org/10.1007/s11856-018-1742-9S8118252272E. Adan-Bante, Products of characters with few irreducible constituents, Journal of Algebra 311 (2007), 38–68.E. Adan-Bante, Symmetric groups and conjugacy classes, Journal of Group Theory 3 (2008), 371–379.Z. Arad and E. Fisman, An analogy between products of two conjugacy classes and products of two irreducible characters in finite groups, Proceedings of the Edinburgh Mathematical Society 30 (1987), 7–22.Z. Arad and M. Herzog, Products of Conjugacy Classes in Groups, Lecture Notes in Mathematics, Vol. 1112, Springer-Verlag, Berlin, 1985.A. Beltrán, M. J. Felipe and C. Melchor, Squares of real conjugacy classes in finite groups, Annali di Matematica Pura ed Applicata 197 (2018), 317–328.R. W. Carter, Finite Groups of Lie Type, Pure and Applied Mathematics (New York), John Wiley & Sons, New York, 1985.The GAP Group, GAP - Groups, Algorithms and Programming, Vers. 4.7.7, 2015, https://doi.org/www.gap-system.orgG. Glauberman, Central elements in core-free groups, Journal of Algebra 4 (1966), 403–420.R. M. Guralnick and G. Navarro, Squaring a conjugacy class and cosets of normal subgroups, Proceedings of the American Mathematical Society 144 (2016), 1939–1945.R. M. Guralnick and G. R. Robinson, On extensions on the Baer–Suzuki theorem, Israel Journal of Mathematics 82 (1993), 281–297.B. Huppert, Character Theory of Finite Groups, De Gruyter Expositions inMathematics, Vol. 25, Walter de Gruyter, Berlin, 1998.I. M. Isaacs, Character Theory of Finite Groups, Pure and Applied Mathematics, Vol. 69, Academic Press, New York–London, 1976.G. Malle, Almost irreducible tensor squares, Communications in in Algebra 27 (1999), 1033–1051.G. O. Michler, Theory of Finite Simple Groups, New Mathematical Monographs, Vol. 8, Cambridge University Press, Cambridge, 2006.J. Moori and H. P. Tong-Viet, Products of conjugacy classes in simple groups, Quaestiones Mathematicae 34 (2011), 433–439

Landau's theorem on conjugacy classes for normal subgroups

Landau's theorem on conjugacy classes asserts that there are only finitely many finite groups, up to isomorphism, with exactly k conjugacy classes for any positive integer k. We show that, for any positive integers n and s, there exist finitely many finite groups G, up to isomorphism, having a normal subgroup N of index n which contains exactly s non-central G-conjugacy classes. Upper bounds for the orders of G and N are obtained; we use these bounds to classify all finite groups with normal subgroups having a small index and few G-classes. We also study the related problems when we consider only the set of G-classes of prime-power order elements contained in a normal subgroup.The results in this paper are part of the third author's Ph.D. thesis at the Jaume I University of Castellon, who is financially supported by a predoctoral grant of the Jaume I University. The research of the first and second authors is supported by the Valencian Government, Proyecto PROMETEOII/2015/011. The first and the third authors are also partially supported by the Jaume I University, grant P11B2015-77.Beltran, A.; Felipe Román, MJ.; Melchor, C. (2016). Landau's theorem on conjugacy classes for normal subgroups. International Journal of Algebra and Computation. 26(7):1453-1466. doi:10.1142/S0218196716500624S1453146626

Methodology for kinematic cycle characterization of vehicles with fixed routes in urban areas

This paper analyses the driving cycles of a fleet of vehicles with predetermined urban itineraries. Most driving cycles developed for such type of vehicles do not properly address variability among itineraries. Here we develop a polygonal driving cycle that assesses each group of related routes, based on microscopic parameters. It measures the kinematic cycles of the routes traveled by the vehicle fleet, segments cycles into micro-cycles, and characterizes their properties, groups them into clusters with homogeneous kinematic characteristics within their specific micro-cycles, and constructs a standard cycle for each cluster. The process is used to study public bus operations in Madrid

Products of groups and class sizes of pi-elements

[EN] We provide structural criteria for some finite factorised groups G = AB when the conjugacy class sizes in G of certain pi-elements in A boolean OR B are either pi-numbers or pi'-numbers, for a set of primes pi. In particular, we extend for products of groups some earlier resultsM. J. Felipe is supported by Proyecto Prometeo II/2015/011, Generalitat Valenciana (Spain). A. Martínez-Pastor is supported by Proyecto MTM 2014-54707-C3-1-P, Ministerio de Economía, Industria y Competitividad (Spain), and by Proyecto Prometeo/2017/057, Generalitat Valenciana (Spain). The results in this paper are part of the V. M. Ortiz Sotomayor Ph.D. thesis, and he acknowledges the predoctoral grant ACIF/2016/170, Generalitat Valenciana (Spain). The authors are also supported by Proyecto PGC2018-096872-B-I00, Ministerio de Ciencia, Innovación y UniversidadesFelipe Román, MJ.; Martínez-Pastor, A.; Ortiz-Sotomayor, VM. (2020). Products of groups and class sizes of pi-elements. Mediterranean Journal of Mathematics. 17(1):1-20. https://doi.org/10.1007/s00009-019-1444-5S120171Amberg, B., Franciosi, S., de Giovanni, F.: Products of Groups. Oxford University Press Inc., New York (1992)Ballester-Bolinches, A., Cossey, J., Li, Y.: Mutually permutable products and conjugacy classes. Monatsh. Math. 170, 305–310 (2013)Ballester-Bolinches, A., Esteban-Romero, R., Asaad, M.: Products of finite groups, vol. 53 of de Gruyter Expositions in Mathematics, Berlin (2010)Beltrán, A., Felipe, M.J.: Prime powers as conjugacy class lengths of $$\pi$$-elements. Bull. Austral. Math. Soc. 69, 317–325 (2004)Beltrán, A., Felipe, M.J., Malle, G., Moretó, A., Navarro, G., Sanus, L., Solomon, R., Tiep, P.H.: Nilpotent and abelian Hall subgroups in finite groups. Trans. Am. Math. Soc. 368, 2497–2513 (2016)Berkovich, Y., Kazarin, L.S.: Indices of elements and normal structure of finite groups. J. Algebra 283, 564–583 (2005)Doerk, K., Hawkes, T.: Finite Soluble Groups, vol. 4 of de Gruyter Expositions in Mathematics, Berlin (1992)Dolfi, S.: Arithmetical conditions on the length of the conjugacy classes of a finite group. J. Algebra 174, 753–771 (1995)Dolfi, S., Pacifici, E., Sanus, L., Spiga, P.: On the orders of zeros of irreducible characters. J. Algebra 321, 345–352 (2009)Felipe, M.J., Martínez-Pastor, A., Ortiz-Sotomayor, V.M.: Prime power indices in factorised groups, Mediterr. J. Math. 14 (6) (2017), article: 225Felipe, M.J., Martínez-Pastor, A., Ortiz-Sotomayor, V.M.: Zeros of irreducible characters in factorised groups. Ann. Mat. Pura Appl. 198, 129–142 (2019)Itô, N.: On finite groups with given conjugate types I. Nagoya Math. J. 6, 17–28 (1953)Navarro, G., Tiep, P.H.: Abelian Sylow subgroups in a finite group. J. Algebra 398, 519–526 (2014)Zhao, X.H., Guo, X.Y., Shi, J.Y.: On the conjugacy class sizes of prime power order $$\pi$$-elements. South. Asian Bull. Math. 35, 735–740 (2011

Determinación de ciclos de conducción en rutas urbanas fijas

Una forma usual para la evaluación del consumo y emisiones de los vehículos es mediante la reproducción de ciclos estándar de conducción. Así pues, es esencial que estos ciclos se ajusten al comportamiento real de los vehículos. Algunos tipos de vehículos presentan ciclos cinemáticos específicos, como son los vehículos que recorren rutas urbanas fijas, para los que suele considerarse que todos los itinerarios comparten características semejantes, lo cual supone una importante limitación. Este artículo presenta una metodología para la construcción de ciclos de conducción poligonales estándar aplicables a estos vehículos, y determinados para cada grupo de rutas de características cinemáticas semejantes. La metodología integra el tratamiento de los datos de operación, agrupamiento de rutas y construcción del ciclo. Los algoritmos han sido aplicados satisfactoriamente sobre una muestra de líneas de autobuses urbanos en Madrid

MicroRNA expression profiling in Imatinib-resistant Chronic Myeloid Leukemia patients without clinically significant ABL1-mutations

The development of Imatinib Mesylate (IM), the first specific inhibitor of BCR-ABL1, has had a major impact in patients with Chronic Myeloid Leukemia (CML), establishing IM as the standard therapy for CML. Despite the clinical success obtained with the use of IM, primary resistance to IM and molecular evidence of persistent disease has been observed in 20-25% of IM treated patients. The existence of second generation TK inhibitors, which are effective in patients with IM resistance, makes identification of predictors of resistance to IM an important goal in CML. In this study, we have identified a group of 19 miRNAs that may predict clinical resistance to IM in patients with newly diagnosed CML

Frequent and simultaneous epigenetic inactivation of TP53 pathway genes in acute lymphoblastic leukemia

Aberrant DNA methylation is one of the most frequent alterations in patients with Acute Lymphoblastic Leukemia (ALL). Using methylation bead arrays we analyzed the methylation status of 807 genes implicated in cancer in a group of ALL samples at diagnosis (n = 48). We found that 154 genes were methylated in more than 10% of ALL samples. Interestingly, the expression of 13 genes implicated in the TP53 pathway was downregulated by hypermethylation. Direct or indirect activation of TP53 pathway with 5-aza-2'-deoxycitidine, Curcumin or Nutlin-3 induced an increase in apoptosis of ALL cells. The results obtained with the initial group of 48 patients was validated retrospectively in a second cohort of 200 newly diagnosed ALL patients. Methylation of at least 1 of the 13 genes implicated in the TP53 pathway was observed in 78% of the patients, which significantly correlated with a higher relapse (p = 0.001) and mortality (p<0.001) rate being an independent prognostic factor for disease-free survival (DFS) (p = 0.006) and overall survival (OS) (p = 0.005) in the multivariate analysis. All these findings indicate that TP53 pathway is altered by epigenetic mechanisms in the majority of ALL patients and correlates with prognosis. Treatments with compounds that may reverse the epigenetic abnormalities or activate directly the p53 pathway represent a new therapeutic alternative for patients with ALL

Curcumin Hybrid Lipid Polymeric Nanoparticles: Antioxidant Activity, Immune Cellular Response, and Cytotoxicity Evaluation.

Poor solubility and short biological half-life present a challenge that needs to be overcome in order to improve the recognized bioactivities of curcumin (CUR), the main phenolic compounds derived from the roots of Curcuma longa. However, drug delivery systems have proven to be an excellent strategy to improve and obtain greater bioavailability. Our previous studies on curcuminoid hybrid nanoparticles have shown promising results by significantly increasing the solubility of desmethoxycurcumin (DMC) and bisdemethoxycurcumin (BDM). In this contribution, we performed a detailed characterization of a CUR as well as in vitro and in vivo studies. The developed method produced CUR loaded nanoparticles with an average size of 49.46 ± 0.80. Moreover, the FT-IR analysis confirmed the encapsulation, and TEM images showed their spherical shape. The NP achieved an encapsulation efficiency greater than 99%. Further, the release studies found that the NPs obtained a significantly higher release than the pure compounds in water. In vivo delayed-type hypersensitivity (DTH) studies showed promising results by enhancing the immune activity response of CUR in NP compared to bulk CUR. Furthermore, we report a significant increase in antioxidant activity for CUR-NP in aqueous solution compared to free CUR. Finally, an important in vitro cytotoxic effect on gastric AGS and colon SW620 adenocarcinoma cell lines was found for CUR-NP while empty carrier nanoparticles are observed to exhibit low cytotoxicity, indicating the potential of these CUR-PLU NPs for further studies to assess their phytotherapeutic applications.National Laboratory of Nanotechnology (LANOTEC).Ministerio de Ciencia, Innovación, Tecnología y Telecomunicaciones (MICITT)Universidad de Costa Rica/[115-C0-001]/UCR/Costa RicaUniversidad de Costa Rica/[115-C1-515]/UCR/Costa RicaUCR::Vicerrectoría de Docencia::Salud::Facultad de Medicina::Escuela de MedicinaUCR::Vicerrectoría de Docencia::Ciencias Básicas::Facultad de Ciencias::Escuela de QuímicaUCR::Vicerrectoría de Docencia::Salud::Facultad de Farmaci

DNA methylation profiles and their relationship with cytogenetic status in adult acute myeloid leukemia

Background: Aberrant promoter DNA methylation has been shown to play a role in acute myeloid leukemia (AML) pathophysiology. However, further studies to discuss the prognostic value and the relationship of the epigenetic signatures with defined genomic rearrangements in acute myeloid leukemia are required. Methodology/Principal Findings: We carried out high-throughput methylation profiling on 116 de novo AML cases and we validated the significant biomarkers in an independent cohort of 244 AML cases. Methylation signatures were associated with the presence of a specific cytogenetic status. In normal karyotype cases, aberrant methylation of the promoter of DBC1 was validated as a predictor of the disease-free and overall survival. Furthermore, DBC1 expression was significantly silenced in the aberrantly methylated samples. Patients with chromosome rearrangements showed distinct methylation signatures. To establish the role of fusion proteins in the epigenetic profiles, 20 additional samples of human hematopoietic stem/progenitor cells (HSPC) transduced with common fusion genes were studied and compared with patient samples carrying the same rearrangements. The presence of MLL rearrangements in HSPC induced the methylation profile observed in the MLL-positive primary samples. In contrast, fusion genes such as AML1/ETO or CBFB/MYH11 failed to reproduce the epigenetic signature observed in the patients. Conclusions/Significance: Our study provides a comprehensive epigenetic profiling of AML, identifies new clinical markers for cases with a normal karyotype, and reveals relevant biological information related to the role of fusion proteins on the methylation signature