Classes de fitting e a secção de Lockett

Tese de mestrado em Matemática, apresentada à Universidade de Lisboa, através da Faculdade de Ciências, 2013O estudo das classes de grupos finitos teve a sua origem com o trabalho de Gaschütz. No entanto, o tema central desta tese serão os conceitos desenvolvidos por Fischer , numa tentativa de dualizar a teoria construída por Gaschütz. Com estas ferramentas, provaremos um teorema importante de Fischer et al., que relaciona as classes de Fitting e os injectores (ambos para o caso dos grupos finitos e resolúveis), previamente introduzidos. Na teoria das classes de Fitting, iremos estudar os trabalhos de Lockett, envolvendo a Secção Lockett e tentando responder a algumas questões acerca da relação entre o produto directo dos radicais e o radical do produto directo, de um grupo finito. Também nesse âmbito, introduziremos brevemente as classes de Fitting normais. No quarto capítulo construiremos o grupo de Lausch e provaremos alguns resultados envolvendo a relação entre este e um par de Fitting dado. Ainda neste capítulo apresentaremos alguns resultados devidos a Lausch e que foram posteriormente generalizados por Bryce and Cossey, envolvendo descrições teóricas, quer da classe F*, quer do radical GF*. A construção de Lausch dar-nos-á então uma ferramenta importante para desenvolvermos o último capítulo. Nesse capítulo, com a ajuda do trabalho desenvolvido por Brison, acerca das ideias de Berger, pretendemos apresentar uma descição mais detalhada do radical GF*.The study of classes of finite groups had its origins with the work of Gaschütz. However, the main focus of this thesis will be on the concepts developed by Fischer, in an attempt to dualize this work. With this tools in hand, we will prove one important theorem of Fischer et al., that relates Fitting classes and injectors (both for the case of finite soluble groups), previously introduced. Within the theory Fitting classes of finite groups, we will study the works of Lockett, envolving the Lockett section, trying to answer some questions about the relation between the direct product of radicals and the radical of the direct product, of a finite group. Also in that scope, we will briey introduce normal Fitting classes. In the fourth chapter we will construct the Lausch group and prove some results involving the relation between it and a given Fitting pair. We also present here some results by Lausch and generalized by Bryce and Cossey, involving some theoretical aproaches to the description of the class F* and the radical GF*. The construction of Lausch will provide us with an important tool to develop in the last chapter. There, with the help of the work developed by Brison, on the ideas of Berger, we aim to deepen the results about the radical GF*, trying to give a more practical description than the previous one

High prevalence of oral potentially malignant disorders and risk factors in a semi-urban brazilian city:a population-based cross-sectional study

Oral Potentially Malignant Disorders (OPMDs) are defined as lesions with a greater likelihood of progressing to cancer. Population-based studies that evaluate the prevalence of OPMDs are scarce in Brazil. The aim of the present study was to determine the prevalence of OPMDs and associated risk factors in a semi-urban Brazilian population. This is a cross-sectional study, whose universe included individuals aged 40 years or older residing in a medium-sized city of northeastern Brazil. Data collection was divided into two steps: interview and oral examination. The outcome variable was the presence of OPMDs. The predictor variables were sociodemographic characteristics and risk habits. The bivariate analysis was performed through chi-square test. The crude prevalence ratios (PR) and its respective 95% confidence intervals (CI) were calculated. Poisson regression analysis with robust variance was used to calculate adjusted PRs and 95% CI. Three hundred fourteen individuals were included in the study. When asked about risk habits, 58.9% reported being current smokers or ex-smokers and 62.2% reported being current drinkers or ex-drinkers. The prevalence of OPMDs was 7.6% and was significantly higher among individuals with black skin color (p < 0.001), alcohol users (p = 0.017), and individuals with both tobacco and alcohol habits (p = 0.012). Therefore, the population in the present study had a high frequency of risk habits associated with PMDs of the oral cavity

Temporomandibular joint disorders in skeletal class II patients referred to orthognathic surgery: A cross-sectional study.

ObjectivesThe aim of this study was to assess the prevalence of Temporomandibular Disorders (TMD) in subjects with skeletal class II dentofacial deformity referred for orthognathic surgery, as well as to elucidate its association with sociodemographic and psychosocial features.MethodsThis was a cross-sectional study using the Research Diagnostic Criteria for Temporomandibular Disorders. The sample comprised class II skeletal patients referred to an Oral and Maxillofacial Surgery center in the Brazilian Northeast.ResultsSeventy-three subjects were enrolled and completed the data collection, which consisted of a physical examination according to Axis I of the Research Diagnostic Criteria for Temporomandibular Disorders and facial analysis. Women represented 82.2% of the sample. Among the assessed subjects, 68.5% were already undergoing orthodontic treatment, and the mean overjet of patients was 6.97 mm. The prevalence of TMD in this sample was 46.6%, with muscular disorders being the most common. Patients with an anteroposterior discrepancy greater than 7 mm showed a higher occurrence of TMD (p = 0.017).ConclusionThis study demonstrated a high prevalence of TMD in skeletal class II patients referred for orthognathic surgery, especially in those with a pronounced overjet, being Group I (muscular disorders) and Group III (degenerative disorders) the most prevalent

S2 Appendix -

Objectives: The aim of this study was to assess the prevalence of Temporomandibular Disorders (TMD) in subjects with skeletal class II dentofacial deformity referred for orthognathic surgery, as well as to elucidate its association with sociodemographic and psychosocial features. Methods: This was a cross-sectional study using the Research Diagnostic Criteria for Temporomandibular Disorders. The sample comprised class II skeletal patients referred to an Oral and Maxillofacial Surgery center in the Brazilian Northeast. Results: Seventy-three subjects were enrolled and completed the data collection, which consisted of a physical examination according to Axis I of the Research Diagnostic Criteria for Temporomandibular Disorders and facial analysis. Women represented 82.2% of the sample. Among the assessed subjects, 68.5% were already undergoing orthodontic treatment, and the mean overjet of patients was 6.97 mm. The prevalence of TMD in this sample was 46.6%, with muscular disorders being the most common. Patients with an anteroposterior discrepancy greater than 7 mm showed a higher occurrence of TMD (p = 0.017). Conclusion: This study demonstrated a high prevalence of TMD in skeletal class II patients referred for orthognathic surgery, especially in those with a pronounced overjet, being Group I (muscular disorders) and Group III (degenerative disorders) the most prevalent.</div

Data extracted during research.

Objectives: The aim of this study was to assess the prevalence of Temporomandibular Disorders (TMD) in subjects with skeletal class II dentofacial deformity referred for orthognathic surgery, as well as to elucidate its association with sociodemographic and psychosocial features. Methods: This was a cross-sectional study using the Research Diagnostic Criteria for Temporomandibular Disorders. The sample comprised class II skeletal patients referred to an Oral and Maxillofacial Surgery center in the Brazilian Northeast. Results: Seventy-three subjects were enrolled and completed the data collection, which consisted of a physical examination according to Axis I of the Research Diagnostic Criteria for Temporomandibular Disorders and facial analysis. Women represented 82.2% of the sample. Among the assessed subjects, 68.5% were already undergoing orthodontic treatment, and the mean overjet of patients was 6.97 mm. The prevalence of TMD in this sample was 46.6%, with muscular disorders being the most common. Patients with an anteroposterior discrepancy greater than 7 mm showed a higher occurrence of TMD (p = 0.017). Conclusion: This study demonstrated a high prevalence of TMD in skeletal class II patients referred for orthognathic surgery, especially in those with a pronounced overjet, being Group I (muscular disorders) and Group III (degenerative disorders) the most prevalent.</div

List of abbreviations.

Objectives: The aim of this study was to assess the prevalence of Temporomandibular Disorders (TMD) in subjects with skeletal class II dentofacial deformity referred for orthognathic surgery, as well as to elucidate its association with sociodemographic and psychosocial features. Methods: This was a cross-sectional study using the Research Diagnostic Criteria for Temporomandibular Disorders. The sample comprised class II skeletal patients referred to an Oral and Maxillofacial Surgery center in the Brazilian Northeast. Results: Seventy-three subjects were enrolled and completed the data collection, which consisted of a physical examination according to Axis I of the Research Diagnostic Criteria for Temporomandibular Disorders and facial analysis. Women represented 82.2% of the sample. Among the assessed subjects, 68.5% were already undergoing orthodontic treatment, and the mean overjet of patients was 6.97 mm. The prevalence of TMD in this sample was 46.6%, with muscular disorders being the most common. Patients with an anteroposterior discrepancy greater than 7 mm showed a higher occurrence of TMD (p = 0.017). Conclusion: This study demonstrated a high prevalence of TMD in skeletal class II patients referred for orthognathic surgery, especially in those with a pronounced overjet, being Group I (muscular disorders) and Group III (degenerative disorders) the most prevalent.</div

Absolute and relative frequencies of subject’s demographics and habits variables.

Absolute and relative frequencies of subject’s demographics and habits variables.</p

Frequencies, Chi-square, <i>p</i>-Value, PR and respective confidence intervals of the outcome "Presence of TMD" associated with independent variables.

Frequencies, Chi-square, p-Value, PR and respective confidence intervals of the outcome "Presence of TMD" associated with independent variables.</p

S1 Appendix -

Objectives: The aim of this study was to assess the prevalence of Temporomandibular Disorders (TMD) in subjects with skeletal class II dentofacial deformity referred for orthognathic surgery, as well as to elucidate its association with sociodemographic and psychosocial features. Methods: This was a cross-sectional study using the Research Diagnostic Criteria for Temporomandibular Disorders. The sample comprised class II skeletal patients referred to an Oral and Maxillofacial Surgery center in the Brazilian Northeast. Results: Seventy-three subjects were enrolled and completed the data collection, which consisted of a physical examination according to Axis I of the Research Diagnostic Criteria for Temporomandibular Disorders and facial analysis. Women represented 82.2% of the sample. Among the assessed subjects, 68.5% were already undergoing orthodontic treatment, and the mean overjet of patients was 6.97 mm. The prevalence of TMD in this sample was 46.6%, with muscular disorders being the most common. Patients with an anteroposterior discrepancy greater than 7 mm showed a higher occurrence of TMD (p = 0.017). Conclusion: This study demonstrated a high prevalence of TMD in skeletal class II patients referred for orthognathic surgery, especially in those with a pronounced overjet, being Group I (muscular disorders) and Group III (degenerative disorders) the most prevalent.</div