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We classify all 2‐blocks with abelian defect groups of rank 4 up to Morita equivalence. The classification holds for blocks over a suitable discrete valuation ring as well as for those over an algebraically closed field. An application is that Broué's abelian defect group conjecture holds for all blocks under consideration here. [ABSTRACT FROM AUTHOR]

Background: Perioperative education and socioeconomic factors influence patient behavior. Recent evidence has suggested that sling compliance is associated with improved outcomes after shoulder surgery; it is important to investigate factors that influence sling compliance. Purpose: To determine the associations between postoperative sling wear and patients' understanding of sling necessity, postoperative home assistance, and social deprivation. Study Design: Cohort study; Level of evidence, 2. Methods: A total of 66 patients were prospectively enrolled from 2018 to 2020 if they were ≥18 years of age and undergoing shoulder surgery requiring a sling for at least 1 month postoperatively. Sling wear was measured using a temperature-sensing device. At 6 weeks postoperatively, patients' understanding for sling necessity was determined by their response to a question on the Medical Adherence Measure questionnaire, "Why did you have to wear a shoulder sling?" The Patient Understanding Grading Scale (PUGS) was developed to quantify patient responses. PUGS was graded 1 to 3, with grade 1 corresponding to the least technical knowledge. Patient characteristics, social deprivation (Area Deprivation Index [ADI]), and home assistance were additionally analyzed. Results: There were no significant differences in baseline characteristics between patients when stratified by PUGS grade. Multivariable linear regression analysis for total hours of sling wear per week showed that patients with PUGS grade 2 (β, 48.2 hours; P =.007) and grade 3 (β, 59.5 hours; P =.003) wore their slings significantly more than grade 1 patients. Patients with home assistance had significantly greater day hours (73.5 ± 33.0 vs 44.0 ± 24.5 hours; P =.037) of sling wear per week, but there was no difference in night sling hours. Patients older than 60 years wore their slings significantly more, while men and those with a higher body mass index (BMI) wore their slings significantly less. ADI was not significantly associated with sling wear. Conclusion: This study demonstrates that patients with greater understanding for sling necessity, those with home assistance, and patients >60 years have greater sling wear, while male patients and those with a higher BMI have lower sling compliance. ADI was not a significant contributor. [ABSTRACT FROM AUTHOR]