Some results on locally finite groups

En esta tesis se presentan algunos resultados sobre p-nilpotencia y permutabilidad en grupos localmente finitos. Está estructurada en cinco capítulos. El primer capítulo, que tiene carácter introductorio: contiene definiciones y resultados conocidos que serán utilizados en los capítulos sucesivos. Por tratarse de resultados ya conocidos, se introducen con referencias y sin demostraciones. En el capítulo 2 se trata la p-nilpotencia en grupos hiperfinitos, donde p es un primo. Los resultados presentados se encuentran publicados en el siguiente artículo: Ballester-Bolinches, A.; Camp-Mora, S.; Spagnuolo, F., "On p-nilpotency of hyperfinite groups". Monatshefte f¨ur Mathematik, 176, no. 4, 497–502, 2015. Un grupo se dice p-nilpotente si tiene un p-subgrupo de Hall normal. En el caso de grupos finitos, se tiene que un grupo es p-nilpotente si y solo si todo p-subgrupo de Sylow tiene un p-complemento normal. En este capítulo se estudian propiedades de los p-subgrupos de Sylow de un grupo que garanticen que el grupo es p-nilpotente si y solo si el normalizador de un p-subgrupo de Sylow es p-nilpotente. Por ejemplo, un resultado clásico de Burnside establece que un grupo finito con p-subgrupos de Sylow abelianos es p-nilpotente si y solo si el normalizador de un p-subgrupo de Sylow es p-nilpotente. Para ello, se define la propiedad de determinación local de p-nilpotencia: una clase de p-grupos X determina la p-nilpotencia localmente si todo grupo finito G con un p-subgrupo de Sylow P en la clase X es p-nilpotente si y solo si el normalizador de P en G es p-nilpotente. Los resultados principales del capítulo 2 extienden varios resultados conocidos sobre p-nilpotencia de grupos finitos. Se prueba que: - Si X es una clase de p-grupos cerrada para subgrupos e imágenes epimorfas que determina la p-nilpotencia localmente y G es un grupo hiperfinito con un p-subgrupo de Sylow pronormal P en la clase X, entonces G es p-nilpotente si y solo si el normalizador de P en G es p-nilpotente. - Si X es una clase de p-grupos cerrada para subgrupos que determina la p-nilpotencia localmente y G es un grupo hiperfinito localmente p-resoluble con un p-subgrupo de Sylow P en la clase X, entonces G es p-nilpotente si y solo si el normalizador de P en G es p-nilpotente. En los capítulos 3 y 4 se estudian grupos de rango infinito en los que el comportamiento de los subgrupos de rango infinito respecto a cierta propiedad determina la estructura del grupo. Los resultados de estos capítulos aparecen en el artículo: Ballester-Bolinches, A.; Camp-Mora, S.; Kurdachenko, L.A.; Spagnuolo, F., "On groups whose subgroups of infinite rank are Sylow permutable". Annali di Matematica Pura ed Applicata (4), 195, no. 3, 717–723, 2016, y en el trabajo: Ballester-Bolinches, A.; Camp-Mora, S.; Dixon, M.R.; Ialenti, R.; Spagnuolo, F., "On locally finite groups whose subroups of infinite rank have some permutable property", aceptado en Annali di Matematica Pura ed Applicata. Recordemos que un grupo G tiene rango finito e igual a r si los subgrupos finitamente generados de G están generados por como máximo r elementos y r es el menor entero con tal propiedad. Si no existe un tal r, se dice que G tiene rango infinito. Se dice que G tiene p-rango de sección finito e igual a r si toda sección p-elemental abeliana de G es finita y tiene orden como máximo p^r y hay una sección p-elemental abeliana con orden exactamente p^r. Igualmente, si no existe un tal r, se dice que G tiene p-rango de sección infinito. Las propiedades de los subgrupos de rango infinito que se consideran son la permutabilidad y algunas generalizaciones de la permutabilidad. En particular, en el capítulo 3 los principales resultados obtenidos se refieren a las propiedades de permutabilidad y permutabilidad con los subgrupos de Sylow. Se prueban los siguientes resultados: - Si en un grupo G hiper-(abeliano o finito) con p-rango de sección infinito todo subgrupo con p-rango de sección infinito es S-permutable, entonces G es localmente nilpotente. - Si en un grupo G localmente finito con rango infinito todo subgrupo de rango infinito es S-permutable, entonces G es localmente nilpotente. - Si en un grupo G localmente finito con p-rango de sección infinito todo subgrupo con p-rango de sección infinito es permutable, entonces G es un grupo de Iwasawa. Como consecuencia de los resultados principales se recuperan algunos resultados ya conocidos. En el capítulo 4 se consideran las propiedades de semipermutabilidad y S- semipermutabilidad. Se prueban los siguientes resultados: - En los grupos localmente finitos con p-rango de sección infinito cuyos subgrupos con p-rango de sección infinitos son semipermutables, todos los subgrupos son semipermutables. - Para la S-semipermutabilidad, se prueba que en un grupo localmente finito con condición minimal sobre los p-subgrupos para todos los primos p, si todos los subgrupos de rango infinito son S-semipermutables, entonces todos los subgrupos son S-semipermutables. Se presenta un contraejemplo que muestra que en el último resultado no se puede eliminar la hipótesis de que el grupo tenga la condición minimal sobre los p-subgrupos para todo primo p. En el capítulo 5 se consideran únicamente grupos finitos y se estudia la inmersión de los subgrupos semimodulares de orden impar en un grupo finito. Un grupo se dice semimodular si todos sus subgrupos son semipermutables. Los resultados forman parte del siguiente trabajo, que ha sido enviado para su posible publicación en una revista científica: Ballester-Bolinches, A.; Heineken, H.; Spagnuolo, F., "On semipermutable subgroups of finite groups", enviado. Algunos de los resultados de este capítulo son los siguientes: - Un grupo finito que es producto de un subgrupo normal superresoluble y de un subgrupo subnormal semimodular es superresoluble. - Si un grupo finito G tiene un subgrupo normal N superresoluble y un subgrupo S subnormal semimodular de orden impar, entonces el producto NS^G es superresoluble. Una consecuencia interesante del último resultado es que la clausura normal de un subgrupo subnormal semimodular de orden impar es superresoluble.The main goal of this thesis is to present some results on p-nilpotency and permutability in locally finite groups. It is organised in five chapters. Well known definitions and results which are widely used in the thesis are collected in the first chapter. They are stated with suitable references. No proofs are included. Chapter two is devoted to the study of p-nilpotency of hyperfinite groups, p a prime. The results are published in the paper: Ballester-Bolinches, A.; Camp-Mora, S.; Spagnuolo, F., "On p-nilpotency of hyperfinite groups". Monatshefte f¨ur Mathematik, 176, no. 4, 497-502, 2015. A group is p-nilpotent if it has a normal Hall p0-subgroup. In finite groups, a group is p-nilpotent if and only if every Sylow p-subgroup has a normal p-complement. In this chapter we study which properties of the Sylow p-subgroups determine the p-nilpotency of the group by the p-nilpotency of their normalisers. For example, a classical result of Burnside states that a finite group G with an abelian Sylow p-subgroup P is p-nilpotent if and only if the normalizer of P in G is p-nilpotent. A class of p-groups X determines p- nilpotency locally if every finite group G with a Sylow p-subgroup P in X is p-nilpotent if and only if the normalizer of P in G is p-nilpotent. The main results of chapter 2 extend some known results of p-nilpotency of finite groups to hyperfinite groups. We prove: - If X is a subgroup closed class of p-groups closed under taking epimorphic images that determines p-nilpotency locally and G is a hyperfinite group with a pronormal Sylow p-subgroup P in the class X, then G is p-nilpotent if and only if the normalizer of P in G is p-nilpotent. - If X is a subgroup closed class of p-groups that determines p-nilpotency locally and G is a hyperfinite locally p-soluble group with a Sylow p-subgroup P in the class X, then G is p-nilpotent if and only if the normalizer of P in G is p-nilpotent. In chapters 3 and 4 we study the structural influence of the subgroups of infinite rank. The results are collected in the following two papers. Ballester-Bolinches, A.; Camp-Mora, S.; Kurdachenko, L.A.; Spagnuolo, F., "On groups whose subgroups of infinite rank are Sylow permutable". Annali di Matematica Pura ed Applicata (4), 195, no. 3, 717-723, 2016, Ballester-Bolinches, A.; Camp-Mora, S.; Dixon, M.R.; Ialenti, R.; Spagnuolo, F., "On locally finite groups whose subroups of infinite rank have some permutable property", accepted for publication in Annali di Matematica Pura ed Applicata. Recall that a group G has finite rank equal to r if every finitely generated subgroup of G is generated by at most r elements and r is the least integer with this property. If such an integer r does not exist then we say that G has infinite rank. Furthermore, G has finite section p-rank equal to r if every elementary abelian p-section of G is finite of order at most p^r and there is an elementary abelian p-section of G of order exactly p^r. As before, if such an integer r does not exist then G has infinite section p-rank. The properties of subgroups we consider includes permutability, S-permutability, semipermutability and S-semipermutability. The main results of Chapter 3 are: - If in a hyper-(abelian or finite) group G with infinite section p-rank all subgroups with infinite section p-rank are S-permutable, then G is locally nilpotent. - If in a locally finite group G with infinite rank all subgroups of infinite rank are S-permutable, then G is locally nilpotent. - If in a locally finite group G with infinite section p-rank all subgroups with infinite section p-rank are permutable, then G is an Iwasawa group. We prove some known results as a consequence of the main theorems. In chapter 4, the properties considered are semipermutability and S- semipermutability. The main results are: - In locally finite groups with infinite section p-rank whose subgroups with infinite section p-rank are semipermutable, all subgroups are semipermutable. - For S-semipermutability, it is proved that in a locally finite group with the minimal condition on p-subgroups for every prime p, if all subgroups with infinite rank are S-semipermutable then all subgroups are S-semipermutable. It is presented a counterexample that shows that the minimal condition on the p-subgroups cannot be omitted. In chapter 5 all groups considered are finite. We study the immersion of semimodular subgroups of odd order in a finite group. The results presented can be found in the following paper, submitted to a scientific journal: Ballester-Bolinches, A.; Heineken, H.; Spagnuolo, F., "On semipermutable subgroups of finite groups". Submitted. Some of the results of this chapter are: - A finite group, product of a normal supersoluble subgroup and a subnormal semimodular subgroup of odd order, is supersoluble. - If a finite group G has a normal supersoluble subgroup N and a subnormal semimodular subgroup of odd order S, then the product NS^G is supersoluble. An interesting consequence of the last result is that the normal closure of a subnormal semimodular subgroup of odd order is supersoluble

Human Periapical Cysts-Mesenchymal Stem Cells Cultured with Allogenic Human Serum are a "clinical-grade" construct alternative to bovine fetal serum and indicated in the regeneration of endo-periodontal tissues

Aim: Our research investigated the use of human serum (HS) as a safe and clinical-grade culture medium, using a new cell-model: hPCy-MSCs. This article is aimed to concretely applicate the concept of "waste-based regenerative dentistry" to translate it in future endo-periodontal applications. Methodology: HPCy-MSCs were cultured in 2 different mediums, both containing α-MEM: the 1st with 10% FBS (Control group), and the 2nd with 10% human serum (Test group).Cell proliferation and stemness assays, gene expression, immunophenotypic analysis and osteogenic differentiation were performed to verify our hypothesis. cDNA samples were amplified with qPCR.Experiments were performed in triplicate and analysed with statistical software. Results: The hPCy-MSCs cultivated in a medium with HS were morphologically similar to those cultivated with FBS, and showed a significantly higher proliferation rate. Von Kossa's staining revealed that osteoblasts from hPCy-MSCs in HS implemented with osteogenic induction factors, showed a better osteogenic activity, also confirmed by a significant upregulation of osteopotin (OPN) and matrix extracellular phosphoglycoprotein (MEPE). Conclusions: HPCy-MSCs cultivated in HS showed phenotypic stability and a clear regenerative binding, thus, suggesting these two components as a clinically-grade construct for future endo-periodontal therapies. Riassunto: Obiettivi: La nostra ricerca ha analizzato l'utilizzo del siero umano (HS) come mezzo di coltura sicuro e "clinical-grade", per uso clinico, utilizzando un nuovo modello cellulare: le hPC-MSCs. Questo articolo ha lo scopo di applicare concretamente il concetto di "odontoiatria rigenerativa basata sui rifiuti biologici", al fine di tradurlo in future applicazioni endo-periodontali. Materiali e metodi: Le HPCy-MSCs sono state coltivate in 2 mezzi di coltura diversi, entrambi contenenti α-MEM: il primo con 10% di FBS (gruppo di controllo) e il secondo con il 10% di siero umano (gruppo di test).Sono stati eseguiti saggi di proliferazione cellulare e di staminalità, espressione genica, analisi immunofenotipica e differenziamento osteogenico per verificare la nostra ipotesi di partenza. Campioni di cDNA sono stati amplificati con qPCR.Gli esperimenti sono stati eseguiti in triplicato e analizzati con software statistici. Risultati: Le hPC-MSC coltivate in un terreno con HS erano morfologicamente simili a quelle coltivate con FBS e mostravano un tasso di proliferazione significativamente più alto. La colorazione di Von Kossa ha rivelato che gli osteoblasti da hPC-MSC coltivate in HS implementato con fattori di induzione osteogenica hanno mostrato una migliore attività osteogenica, confermata anche da una significativa up-regolazione di osteopotina (OPN) e fosfoglicoproteina della matrice extracellulare (MEPE). Conclusioni: Le HPCy-MSC coltivate in HS hanno mostrato stabilità fenotipica e un chiaro atteggiamento rigenerativo, suggerendo quindi questo protocollo come un approccio clinicamente valido per le future terapie endo-periodontali. Keywords: Regenerative medicine, Stem cells, Osteogenesis, Human periapical cyst-MSCs, Translational research, Parole chiave: Medicina rigenerativa, Cellule staminali, Osteogenesi, Human periapical cyst-MSCs, Ricerca traslazional

Implantation of a Small Aperture Intraocular Lens in Eyes with Irregular Corneas and Higher Order Aberrations

Purpose: Corneal irregularities can lead to high order aberrations (HOAs) and may influence the outcomes in terms of intraocular lens (IOL) selection and visual acuity assessment. The aim of this study was to evaluate the visual acuity and satisfaction after IC-8 implants in patients characterized by corneal irregularities and HOAs who could not undergo refractive surgery due to the poor residual thickness of the cornea or other conditions such as astigmatism secondary to previous radial keratotomy. Methods: This descriptive, retrospective cohort study was conducted on nine eyes in six patients affected by corneal irregularities and HOAs who had undergone IC-8 IOL implantation. The primary endpoint was the best-corrected visual acuity (BCVA), the subjective visual function, and the visual field. Results: Nine eyes of six patients (three bilateral implantation) were enrolled. For each patient, BCVA, vision, and lifestyle quality were evaluated. In all patients, we noticed an improvement in all parameters without visual field defects. Conclusion: Our work encourages the use of the IC8 lens to improve visual acuity in patients with irregular corneas and HOAs who cannot be treated with customized refractive surgery. Patients experience a subjective improvement of their quality of vision and also more self-confidence in their daily life. IC-8 lenses do not interfere with the visualization of retinal fundus and there is no impairment of the visual field detected by patients

Testing the improvement of ShakeMaps using f inite-f ault models and synthetic seismograms

ShakeMap package uses empirical ground motion prediction equations (GM PEs) to estimate the ground motion where recorded data are not available. Recorded and estimated values are then interpolated in order to produce a shaking map associated to the considered event. Anyway GMPEs account only for average characteristics of source and wave propagation processes. Within the framework of the DPC-INGV S3 project (2007-09), we evaluate whether the inclusion of directivity effects in GMPEs (companion paper Spagnuolo et al., 2010) or the use of synthetic seismograms from finite-fault rupture models may improve the ShakeMap evaluation. An advantage of using simulated motions from kinematic rupture models is that source effects, as rupture directivity, are directly included in the synthetics. This is particularly interesting in Italy where the regional GMPEs, based on a few number of near-source records for moderate-to-large earthquakes, are not reliable for estimating ground motion in the vicinity of the source. In this work we investigated how and if the synthetic seismograms generated with finite-fault models can be used in place of (or in addition to) GMPEs within the ShakeMap methodology. We assumed a description of the rupture model with gradually increasing details, from a simple point source to a kinematic rupture history obtained from inversion of strong-motion data. According to the available information synthetic seismograms are calculated with methods that account for the different degree of approximation in source properties. We chose the M w 6.9 2008 Iwate-M iyagi (Japan) earthquake as a case study. This earthquake has been recorded by a very large number of stations and the corresponding ShakeMap relies almost totally on the recorded ground motions. Starting from this ideal case, we removed a number of stations in order to evaluate the deviations from the reference map and the sensitivity of the map to the number of stations used. The removed data are then substituted with synthetic values calculated assuming different source approximations, and the resulting maps are compared to the original ones (containing observed data only). The use of synthetic seismograms computed for finite-fault rupture models produces, in general, an improvement of the calculated ShakeMaps, especially when synthetics are used to integrate real data. When real data are not available and ShakeMap is estimated using GMPEs only, the improvement adding simulated values depends on the considered strong-motion parameters

Impact of analytical treatment interruption on burden and diversification of HIV peripheral reservoir: a pilot study

Background: If analytical antiretroviral-treatment (ART) interruption (ATI) might significantly impact quantitative or qualitative peripheral-total HIV-DNA is still debated. Methods: Six chronically HIV-1 infected patients enrolled in APACHE-study were analysed for peripheral-total HIV-DNA and residual viremia, major-resistance-mutations (MRMs) and C2-V3-C3 evolution at pre-ATI (T1), during ATI (T2) and at achievement of virological success after ART-resumption (post-ATI, T3). These data were obtained at three comparable time-points in five chronically HIV-1 infected patients on suppressive ART for ≥1 year, enrolled in MODAt-study. Results: At T1, APACHE and MODAt individuals had similar peripheral-total HIV-DNA and residual viremia (p = 0.792 and 0.662, respectively), and no significant changes for these parameters were observed between T1 and T3 in both groups. At T1, 4/6 APACHE and 2/5 MODAt carried HIV-DNA MRMs. MRMs disappeared at T3 in 3/4 APACHE. All disappearing MRMs were characterized by T1 intra-patient prevalence <80%, and mainly occurred in APOBEC3-related sites. All MRMs persisted over-time in the 2 MODAt. C2-V3-C3 genetic-distance significantly changed from T1 to T3 in APACHE individuals (+0.36[0.11-0.41], p = 0.04), while no significant changes were found in MODAt. Accordingly, maximum likelihood trees (bootstrap > 70%) and genealogical sorting indices (GSI > 0.50 with p-value < 0.05) showed that T1 C2-V3-C3 DNA sequences were distinct from T2 and T3 viruses in 4/6 APACHE. Virus populations at all three time-points were highly interspersed in MODAt. Conclusions: This pilot study indicates that short ATI does not alter peripheral-total HIV-DNA burden and residual viremia, but in some cases could cause a genetic diversification of peripheral viral reservoir in term of both MRMs rearrangement and viral evolution

High Risk of Secondary Infections Following Thrombotic Complications in Patients With COVID-19

Background. This study’s primary aim was to evaluate the impact of thrombotic complications on the development of secondary infections. The secondary aim was to compare the etiology of secondary infections in patients with and without thrombotic complications. Methods. This was a cohort study (NCT04318366) of coronavirus disease 2019 (COVID-19) patients hospitalized at IRCCS San Raffaele Hospital between February 25 and June 30, 2020. Incidence rates (IRs) were calculated by univariable Poisson regression as the number of cases per 1000 person-days of follow-up (PDFU) with 95% confidence intervals. The cumulative incidence functions of secondary infections according to thrombotic complications were compared with Gray’s method accounting for competing risk of death. A multivariable Fine-Gray model was applied to assess factors associated with risk of secondary infections. Results. Overall, 109/904 patients had 176 secondary infections (IR, 10.0; 95% CI, 8.8–11.5; per 1000-PDFU). The IRs of secondary infections among patients with or without thrombotic complications were 15.0 (95% CI, 10.7–21.0) and 9.3 (95% CI, 7.9–11.0) per 1000-PDFU, respectively (P = .017). At multivariable analysis, thrombotic complications were associated with the development of secondary infections (subdistribution hazard ratio, 1.788; 95% CI, 1.018–3.140; P = .043). The etiology of secondary infections was similar in patients with and without thrombotic complications. Conclusions. In patients with COVID-19, thrombotic complications were associated with a high risk of secondary infections