Double Chain Conditions in Group Theory

Along this work a triadic structure is going to be exhibited, so that each chapter will concern a subgroup property theta and will show fundamental or useful results about the maximal and the minimal condition on theta-subgroups, then moving on to the related double chain condition and showing the behavior of several reasonable classes of groups satisfying it, in comparison with the results for the other two conditions, which it extends

A History of Group Theory through the Lives of Group Theorists: Sophus Lie - Part 1

We continue here our attempt of a systematic historical account of Group Theory inspected by means of the lives and the works of its main actors. The aim is to bring the interested reader through orig- inal correspondences, published and unpublished works, historical perspectives, diatribes and friendships. This issue contains the translation of a memory of Sophus Lie writ- ten by Ludwig Sylow. It was published in the 1899 issue of Archiv for Mathematik of Naturvidenskab soon after Lie’s death. We are grateful to Gunnar Traustason for his translation from Nor- wegian

The Role of Attitudes Toward Medication and Treatment Adherence in the Clinical Response to LAIs: Findings From the STAR Network Depot Study

Background: Long-acting injectable (LAI) antipsychotics are efficacious in managing psychotic symptoms in people affected by severe mental disorders, such as schizophrenia and bipolar disorder. The present study aimed to investigate whether attitude toward treatment and treatment adherence represent predictors of symptoms changes over time. Methods: The STAR Network \u201cDepot Study\u201d was a naturalistic, multicenter, observational, prospective study that enrolled people initiating a LAI without restrictions on diagnosis, clinical severity or setting. Participants from 32 Italian centers were assessed at three time points: baseline, 6-month, and 12-month follow-up. Psychopathological symptoms, attitude toward medication and treatment adherence were measured using the Brief Psychiatric Rating Scale (BPRS), the Drug Attitude Inventory (DAI-10) and the Kemp's 7-point scale, respectively. Linear mixed-effects models were used to evaluate whether attitude toward medication and treatment adherence independently predicted symptoms changes over time. Analyses were conducted on the overall sample and then stratified according to the baseline severity (BPRS < 41 or BPRS 65 41). Results: We included 461 participants of which 276 were males. The majority of participants had received a primary diagnosis of a schizophrenia spectrum disorder (71.80%) and initiated a treatment with a second-generation LAI (69.63%). BPRS, DAI-10, and Kemp's scale scores improved over time. Six linear regressions\u2014conducted considering the outcome and predictors at baseline, 6-month, and 12-month follow-up independently\u2014showed that both DAI-10 and Kemp's scale negatively associated with BPRS scores at the three considered time points. Linear mixed-effects models conducted on the overall sample did not show any significant association between attitude toward medication or treatment adherence and changes in psychiatric symptoms over time. However, after stratification according to baseline severity, we found that both DAI-10 and Kemp's scale negatively predicted changes in BPRS scores at 12-month follow-up regardless of baseline severity. The association at 6-month follow-up was confirmed only in the group with moderate or severe symptoms at baseline. Conclusion: Our findings corroborate the importance of improving the quality of relationship between clinicians and patients. Shared decision making and thorough discussions about benefits and side effects may improve the outcome in patients with severe mental disorders

COVID-19 Severity in Multiple Sclerosis: Putting Data Into Context

Background and objectives: It is unclear how multiple sclerosis (MS) affects the severity of COVID-19. The aim of this study is to compare COVID-19-related outcomes collected in an Italian cohort of patients with MS with the outcomes expected in the age- and sex-matched Italian population. Methods: Hospitalization, intensive care unit (ICU) admission, and death after COVID-19 diagnosis of 1,362 patients with MS were compared with the age- and sex-matched Italian population in a retrospective observational case-cohort study with population-based control. The observed vs the expected events were compared in the whole MS cohort and in different subgroups (higher risk: Expanded Disability Status Scale [EDSS] score > 3 or at least 1 comorbidity, lower risk: EDSS score ≤ 3 and no comorbidities) by the χ2 test, and the risk excess was quantified by risk ratios (RRs). Results: The risk of severe events was about twice the risk in the age- and sex-matched Italian population: RR = 2.12 for hospitalization (p < 0.001), RR = 2.19 for ICU admission (p < 0.001), and RR = 2.43 for death (p < 0.001). The excess of risk was confined to the higher-risk group (n = 553). In lower-risk patients (n = 809), the rate of events was close to that of the Italian age- and sex-matched population (RR = 1.12 for hospitalization, RR = 1.52 for ICU admission, and RR = 1.19 for death). In the lower-risk group, an increased hospitalization risk was detected in patients on anti-CD20 (RR = 3.03, p = 0.005), whereas a decrease was detected in patients on interferon (0 observed vs 4 expected events, p = 0.04). Discussion: Overall, the MS cohort had a risk of severe events that is twice the risk than the age- and sex-matched Italian population. This excess of risk is mainly explained by the EDSS score and comorbidities, whereas a residual increase of hospitalization risk was observed in patients on anti-CD20 therapies and a decrease in people on interferon

Clinical features and outcomes of elderly hospitalised patients with chronic obstructive pulmonary disease, heart failure or both

Background and objective: Chronic obstructive pulmonary disease (COPD) and heart failure (HF) mutually increase the risk of being present in the same patient, especially if older. Whether or not this coexistence may be associated with a worse prognosis is debated. Therefore, employing data derived from the REPOSI register, we evaluated the clinical features and outcomes in a population of elderly patients admitted to internal medicine wards and having COPD, HF or COPD + HF. Methods: We measured socio-demographic and anthropometric characteristics, severity and prevalence of comorbidities, clinical and laboratory features during hospitalization, mood disorders, functional independence, drug prescriptions and discharge destination. The primary study outcome was the risk of death. Results: We considered 2,343 elderly hospitalized patients (median age 81 years), of whom 1,154 (49%) had COPD, 813 (35%) HF, and 376 (16%) COPD + HF. Patients with COPD + HF had different characteristics than those with COPD or HF, such as a higher prevalence of previous hospitalizations, comorbidities (especially chronic kidney disease), higher respiratory rate at admission and number of prescribed drugs. Patients with COPD + HF (hazard ratio HR 1.74, 95% confidence intervals CI 1.16-2.61) and patients with dementia (HR 1.75, 95% CI 1.06-2.90) had a higher risk of death at one year. The Kaplan-Meier curves showed a higher mortality risk in the group of patients with COPD + HF for all causes (p = 0.010), respiratory causes (p = 0.006), cardiovascular causes (p = 0.046) and respiratory plus cardiovascular causes (p = 0.009). Conclusion: In this real-life cohort of hospitalized elderly patients, the coexistence of COPD and HF significantly worsened prognosis at one year. This finding may help to better define the care needs of this population

DMTs and Covid-19 severity in MS: a pooled analysis from Italy and France

We evaluated the effect of DMTs on Covid-19 severity in patients with MS, with a pooled-analysis of two large cohorts from Italy and France. The association of baseline characteristics and DMTs with Covid-19 severity was assessed by multivariate ordinal-logistic models and pooled by a fixed-effect meta-analysis. 1066 patients with MS from Italy and 721 from France were included. In the multivariate model, anti-CD20 therapies were significantly associated (OR = 2.05, 95%CI = 1.39–3.02, p < 0.001) with Covid-19 severity, whereas interferon indicated a decreased risk (OR = 0.42, 95%CI = 0.18–0.99, p = 0.047). This pooled-analysis confirms an increased risk of severe Covid-19 in patients on anti-CD20 therapies and supports the protective role of interferon

On Groups in Which Many Automorphisms Are Cyclic

Let G be a group. An automorphism α of G is said to be a cyclic automorphism if the subgroup 〈x, xα 〉 is cyclic for every element x of G. In [F. de Giovanni, M.L. Newell, A. Russo: On a class of normal endomorphisms of groups, J. Algebra and its Applications 13, (2014), 6pp] the authors proved that every cyclic automorphism is central, namely, that every cyclic automorphism acts trivially on the factor group G/Z(G). In this paper, the class FW of groups in which every element induces by conjugation a cyclic automorphism on a (normal) subgroup of finite index will be investigated