2-Engel relations between subgroups

In this paper we study groups G generated by two subgroups A and B such that is nilpotent of class at most 2 for all a¿. A and b¿. B. A detailed description of the structure of such groups is obtained, generalizing the classical result of Hopkins and Levi on 2-Engel groups

Products of finite connected subgroups

For a non-empty class of groups L, a finite group G = AB is said to be an L-connected product of the subgroups A and B if e L for all a e A and b e B. In a previous paper, we prove that, for such a product, when L = S is the class of finite soluble groups, then [A, B] is soluble. This generalizes the theorem of Thompson that states the solubility of finite groups whose two-generated subgroups are soluble. In the present paper, our result is applied to extend to finite groups previous research about finite groups in the soluble universe. In particular, we characterize connected products for relevant classes of groups, among others, the class of metanilpotent groups and the class of groups with nilpotent derived subgroup. Additionally, we give local descriptions of relevant subgroups of finite groups

2-Engel relations between subgroups

In this paper we study groups G generated by two subgroups A and B such that is nilpotent of class at most 2 for all a¿. A and b¿. B. A detailed description of the structure of such groups is obtained, generalizing the classical result of Hopkins and Levi on 2-Engel groups

Efectividad del programa SolSano en los hábitos, conocimientos y actitudes en materia de fotoprotección de los universitarios

Antecedentes y objetivo El proyecto SolSano es un proyecto educativo escolar que se realiza en Aragón desde el año 2000 y que ha demostrado promover hábitos de protección solar y aumentar conocimientos en los niños a corto plazo. El objetivo de este estudio es valorar la efectividad del programa SolSano a largo plazo. Sujetos y métodos Estudio analítico observacional de cohortes retrospectivo realizado en alumnos de la Universidad de Zaragoza durante el curso 2015-2016. El instrumento de valoración fue un cuestionario validado y adaptado para nuestro objetivo al que accedían a través de Internet. Se realizó una descripción univariante, así como un análisis bivariante y multivariante para estudiar las diferencias entre los participantes que habían estudiado Educación Primaria en un centro escolar donde se realizaba SolSano o no. Resultados Trescientos veinticuatro estudiantes universitarios participaron. La edad media fue 22, 9 años, un 78% de respuestas procedieron de mujeres. El 44% había acudido a un centro donde se realizó el programa SolSano. El 50, 5% de los estudiantes habían sufrido 1 o 2 quemaduras solares el verano anterior. Solo se observaron diferencias estadísticamente significativas en algunos aspectos entre los que asistieron a centros educativos donde se desarrolló el programa SolSano y los que asistieron a otros centros. Conclusión Es el primer estudio para valorar la efectividad de un programa educativo escolar en materia de fotoprotección a largo plazo (15 años). La falta de continuidad del programa en la adolescencia y la existencia de campañas de fotoprotección fuera de la escuela son posibles causas de la ausencia de diferencias en nuestra muestra

Legume consumption is inversely associated with type 2 diabetes incidence in adults: A prospective assessment from the PREDIMED study

Background & aims: Legumes, a low-energy, nutrient-dense and low glycemic index food, have shown beneficial effects on glycemic control and adiposity. As such, legumes are widely recommended in diabetic diets, even though there is little evidence that their consumption protects against type 2 diabetes. Therefore the aim of the present study was to examine the associations between consumption of total legumes and specific subtypes, and type 2 diabetes risk. We also investigated the effect of theoretically substituting legumes for other protein- or carbohydrate-rich foods. Methods: Prospective assessment of 3349 participants in the PREvención con DIeta MEDiterránea (PREDIMED) study without type 2 diabetes at baseline. Dietary information was assessed at baseline and yearly during follow-up. We used Cox regression models to estimate hazard ratios (HRs) and 95% confidence intervals (95% CIs) for type-2 diabetes incidence according to quartiles of cumulative average consumption of total legumes, lentils, chickpeas, dry beans and fresh peas. Results: During a median follow-up of 4.3 years, 266 new cases of type 2 diabetes occurred. Individuals in the highest quartile of total legume and lentil consumption had a lower risk of diabetes than those in the lowest quartile (HR: 0.65; 95% CI: 0.43, 0.96; P-trend = 0.04; and HR: 0.67; 95% CI: 0.46–0.98; P-trend = 0.05, respectively). A borderline significant association was also observed for chickpeas consumption (HR 0.68; 95% CI: 0.46, 1.00; P-trend = 0.06). Substitutions of half a serving/day of legumes for similar servings of eggs, bread, rice or baked potato was associated with lower risk of diabetes incidence. Conclusions: A frequent consumption of legumes, particularly lentils, in the context of a Mediterranean diet, may provide benefits on type 2 diabetes prevention in older adults at high cardiovascular risk. Trial registration: The trial is registered at http://www.controlled-trials.com (ISRCTN35739639). Registration date: 5th October 2005.The authors disclose no conflict of interest related with the article. Centro de Investigación Biomédica en Red Fisiopatología de la Obesidad y Nutrición (CIBEROBN) is an initiative of the Instituto de Salud Carlos III (ISCIII) of Spain which is supported by FEDER funds (CB06/03). Supported by the official funding agency for biomedical research of the Spanish government, ISCIII, through grants provided to research networks specifically developed for the trial (RTIC G03/140 and RD 06/0045) through CIBEROBN, and by grants from Centro Nacional de Investigaciones Cardiovasculares (CNIC 06/2007), Fondo de Investigación Sanitaria–FondoEuropeo de Desarrollo Regional (PI04–2239, PI05/2584, CP06/00100, PI07/0240, PI07/1138, PI07/0954, PI 07/0473, PI10/01407, PI10/02658, PI11/01647, and PI11/02505; PI13/00462), Ministerio de Ciencia e Innovación (AGL-2009–13906-C02 and AGL2010–22319-C03), Fundación Mapfre 2010, Consejería de Salud de la Junta de Andalucía (PI0105/2007), Public Health Division of the Department of Health of the Autonomous Government of Catalonia, Generalitat Valenciana (ACOMP06109, GVA-COMP2010–181, GVACOMP2011–151, CS2010-AP-111, and CS2011-AP-042), and the Navarra Regional Government (27/2011). The Fundación Patrimonio Comunal Olivarero and Hojiblanca SA (Málaga, Spain), California Walnut Commission (Sacramento, CA), Borges SA (Reus, Spain), and Morella Nuts SA (Reus, Spain) donated the olive oil, walnuts, almonds, and hazelnuts, respectively, used in the study. None of the funding sources played a role in the design, collection, analysis or interpretation of the data or in the decision to submit the manuscript for publication. Acknowledgements: The authors thank all the participants for their collaboration, all the PREDIMED personnel for their assistance and all the personnel of affiliated primary care centers for making the study possible. CIBEROBN is an initiative of ISCIII, Spain.Peer Reviewe