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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: Operative management of minimally displaced lateral compression type-1 (LC1) pelvic ring injuries remains controversial. We aimed to assess the proportion of LC1 pelvic fractures that displaced following nonoperative management as a function of specific ring fracture patterns, and we quantified the magnitude of this displacement. Methods: A retrospective review of the billing registry of a level-I trauma center was performed. Two hundred and seventy-three patients with a high-energy LC1 pelvic ring fracture and <5 mm of sacral displacement were included. The fracture pattern was characterized with use of computed tomography (CT) scans and radiographs. Absolute and interval pelvic ring displacement were quantified with use of previously described methodology. Results: Thirty-five pelvic ring injuries (13%) were displaced. The rate of displacement was 31% (15 of 49) for LC1 injuries involving a complete sacral fracture and bilateral ramus fractures, 12% (7 of 58) for injuries involving a complete sacral fracture and a unilateral ramus fracture, and 10% (5 of 52) for injuries involving an incomplete sacral fracture and bilateral ramus fractures. In displaced injuries, the average interval displacement was 4.2mm (95% confidence interval [CI], 1.8 to 6.8) and the final displacement was 9.9 mm ± 4.2 mm. Conclusions: Our study suggests that fracture characteristics can be used to predict the likelihood of displacement of LC1 fractures that are treated without surgery. To our knowledge, the present study is the first to describe the magnitude of displacement that may occur in association with LC1 pelvic ring injuries that are treated nonoperatively; however, further studies are needed to determine the clinical impact of this displacement. Level of Evidence: Diagnostic Level IV. See Instructions for Authors for a complete description of levels of evidence. [ABSTRACT FROM AUTHOR]

This article contributes to an 'historical turn' in security scholarship. It addresses imbalance in security studies' attention to historical empirics, and argues against notions of temporal disjunct prevalent within the discipline. I employ a genealogical framework to clarify the interpellation of past and present; and I introduce the 'conceptual archive' as a lens for pursuing that interpellation in research. My thesis on the 'conceptual archive' represents a twofold contribution. Firstly, a conceptual contribution: I advance the 'conceptual archive' as a way of thinking about past-present interpellation (specifically, existing conceptual logics' remodelling in arguments justifying new practice). Secondly, an analytical contribution: I propose the 'conceptual archive' as a tool for doing genealogy (a research programme with historicising promise, but one suffering nebulous operationalisation at present). I use the field of terrorism studies as an entry-point to these contributions: adopting a mixed-methods research design to trace British counterterrorism practices' roots within an 'archive' of logics on Northern Ireland. I find 1970s British governments remodelled long-standing 'archival' vocabularies in their arguments for new security provisions: framing exceptional practices according to an accepted fabric of concepts. [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]

It is an open problem as to whether any bimodule inducing a Morita auto-equivalence of a block must have endopermutation source. We prove that, for blocks b with normal defect groups in odd characteristic, a stronger result holds, namely that all such bimodules have linear source. We also prove the analogous result in characteristic 2, provided that the defect group is of a specific, slightly restrictive, form. [ABSTRACT FROM AUTHOR]

We construct blocks of finite groups with arbitrarily large O -Morita Frobenius numbers. There are no known examples of two blocks defined over O , with isomorphic defect groups, that are not Morita equivalent but the corresponding blocks defined over k are. Therefore, the above strongly suggests that Morita Frobenius numbers are also unbounded, which would answer a question of Benson and Kessar. [ABSTRACT FROM AUTHOR]

We consider Donovan's conjecture in the context of blocks of groups G with defect group D and normal subgroups N ◁ G such that G = C D (D ∩ N) N , extending similar results for blocks with abelian defect groups. As an application we show that Donovan's conjecture holds for blocks with defect groups of the form Q 8 × C 2 n or Q 8 × Q 8 defined over a discrete valuation ring. [ABSTRACT FROM AUTHOR]

We prove that if b is a block of a finite group with normal abelian defect group and inertial quotient a direct product of elementary abelian groups, then Picent (b) is trivial. We also provide examples of blocks b of finite groups with non-trivial Picent (b). We even have examples with normal abelian defect group and abelian inertial quotient. [ABSTRACT FROM AUTHOR]

Let b be a block with normal abelian defect group and abelian inertial quotient. We prove that every Morita auto-equivalence of b has linear source. We note that this improves upon results of Zhou and also Boltje, Kessar and Linckelmann. [ABSTRACT FROM AUTHOR]

We calculate examples of Picard groups for 2-blocks with abelian defect groups with respect to a complete discrete valuation ring. These include all blocks with abelian 2-groups of 2-rank at most three with the exception of the principal block of J 1. In particular this shows directly that all such Picard groups are finite and Picent, the group of Morita auto-equivalences fixing the centre, is trivial. These are amongst the first calculations of this kind. Further we prove some general results concerning Picard groups of blocks with normal defect groups as well as some other cases. [ABSTRACT FROM AUTHOR]

We give a reduction of Donovan's conjecture for abelian groups to a similar statement for quasisimple groups. Consequently we show that Donovan's conjecture holds for abelian 2-groups. [ABSTRACT FROM AUTHOR]

Abstract We define a new invariant for a p -block of a finite group, the strong Frobenius number, which we use to address the problem of reducing Donovan's conjecture to normal subgroups of index p. As an application we use the strong Frobenius number to complete the proof of Donovan's conjecture for 2-blocks with abelian defect groups of rank at most 4 and for 2-blocks with abelian defect groups of order at most 64. [ABSTRACT FROM AUTHOR]

Abstract In this paper we classify all blocks with defect group C 2 n × C 2 × C 2 up to Morita equivalence. Together with a recent paper of Wu, Zhang and Zhou, this completes the classification of Morita equivalence classes of 2-blocks with abelian defect groups of rank at most 3. The classification holds for blocks over a suitable discrete valuation ring as well as for those over an algebraically closed field. The case considered in this paper is significant because it involves comparison of Morita equivalence classes between a group and a normal subgroup of index 2, so requires novel reduction techniques which we hope will be of wider interest. We note that this also completes the classification of blocks with abelian defect groups of order dividing 16 up to Morita equivalence. A consequence is that Broue's abelian defect group conjecture holds for all blocks mentioned above. [ABSTRACT FROM AUTHOR]

We consider p-blocks with abelian defect groups and in the first part prove a relationship between its Loewy length and that for blocks of normal subgroups of index p. Using this, we show that if B is a 2-block of a finite group with abelian defect group D ≅= C2a1 × ·· ·×C2ar × (C2)8, where ai > 1 for all i and r ≥ 0, then d < LL(B) ≤ 2a1 + · · · + 2ar + 2s - r + 1, where |D| = 2d. When s = 1 the upper bound can be improved to 2a1 +· · ·+ 2ar + 2 - r. Together these give sharp upper bounds for every isomorphism type of D. A consequence is that when D is an abelian 2-group the Loewy length is bounded above by |D| except when D is a Klein-four group and B is Morita equivalent to the principal block of A5. We conjecture similar bounds for arbitrary primes and give evidence that it holds for principal 3-blocks. [ABSTRACT FROM AUTHOR]

Let q be a power of a prime, ℓ a prime not dividing q , d a positive integer coprime to both ℓ and the multiplicative order of q mod ℓ and n a positive integer. A. Watanabe proved that there is a perfect isometry between the principal ℓ -blocks of GL n ( q ) and GL n ( q d ) where the correspondence of characters is given by Shintani descent. In the same paper Watanabe also proved that if ℓ and q are odd and ℓ does not divide | GL n ( q 2 ) | / | U n ( q ) | then there is a perfect isometry between the principal ℓ -blocks of U n ( q ) and GL n ( q 2 ) with the correspondence of characters also given by Shintani descent. R. Kessar extended this first result to all unipotent blocks of GL n ( q ) and GL n ( q d ) . In this paper we extend this second result to all unipotent blocks of U n ( q ) and GL n ( q 2 ) . In particular this proves that any two unipotent blocks of U n ( q ) at unitary primes (for possibly different n ) with the same weight are perfectly isometric. We also prove that this perfect isometry commutes with Deligne–Lusztig induction at the level of characters. [ABSTRACT FROM AUTHOR]

W. Turner has proved that Broué's abelian defect group conjecture holds for certain unipotent blocks of the finite general linear group, the so-called Rouquier blocks. This together with theorems of A. Marcus and of J. Chuang and R. Rouquier proves that the conjecture holds for all blocks of such groups. We prove that other finite classical groups also possess analogues of Rouquier blocks at linear primes. [ABSTRACT FROM AUTHOR]

Purpose: Symptomatic rheumatoid arthritis (RA) can be addressed surgically with open procedures or elbow arthroscopy. Previous studies comparing outcomes of open to arthroscopic arthrolysis for the management of RA did not utilize a large database study. The aim was to compare demographics and two-year complications, in RA patients undergoing open or arthroscopic elbow arthrolysis. Methods: A retrospective, cohort study was performed utilizing a private, nationwide, all-payer database. We queried the database to identify patients undergoing open (n = 578) or arthroscopic (n = 379) arthrolysis for elbow RA. The primary goal of the study was to compare complications at two-years. Categorical variables were assessed utilizing the chi-squared test; while, continuous variables were analyzed using the Student's t-test. Multivariable logistic regression was performed to assess risk factors for infection following open or arthroscopic arthrolysis. Results: RA patients undergoing open elbow arthrolysis were older (55 vs. 49 years, p < 0.001), predominately female (61.6% vs 60.9%, p = 0.895), and likely to have chronic kidney disease (20.4 vs. 12.9%), and DM (45.2 vs. 32.2%) (both p < 0.005). Open elbow arthrolysis was also associated with higher rates of infection (31.7 vs. 4.7%) and wound complications (26.8 vs. 3.4%) (both p = 0.001). Nerve injury rates were found to be similar (8.3 vs. 9.0%, p = 0.81). On multivariable logistic regression, open elbow procedures were associated with the highest risk for infection (OR: 8.43). Conclusions: Patients undergoing open arthrolysis for RA were at a higher risk of infection and wound complications compared to arthroscopic arthrolysis utilizing a nationally representative database. While there appears to be a difference in outcomes following these two procedures, higher level evidence is needed to draw more definitive conclusions. Level of Evidence: Retrospective, Level III [ABSTRACT FROM AUTHOR]

We show that the Green correspondence induces an injective group homomorphism from the linear source Picard group L (B) of a block B of a finite group algebra to the linear source Picard group L (C) , where C is the Brauer correspondent of B. This homomorphism maps the trivial source Picard group T (B) to the trivial source Picard group T (C). We show further that the endopermutation source Picard group E (B) is bounded in terms of the defect groups of B and that when B has a normal defect group E (B) = L (B). Finally we prove that the rank of any invertible B -bimodule is bounded by that of B. [ABSTRACT FROM AUTHOR]

Introduction: An increasing number of states are beginning to legalize recreational cannabis use, and as such, more patients using cannabis are undergoing shoulder arthroplasty procedures. The present study sought to examine the impact of cannabis use on post-operative outcomes. The primary outcomes of interest were postoperative complications, which included infection, periprosthetic fractures, periprosthetic joint infections (PJI), dislocations, and aseptic loosening as well as medical complications. Secondary outcomes were risk factors for PJI and aseptic loosening at two-years. Methods: A private, nationwide, all-payer database (Pearldiver Technologies) was queried to identify shoulder arthroplasty patients from 2010 to 2020. Those not using tobacco or cannabis ("control", n = 10,000), tobacco users (n = 10,000), cannabis users (n = 155), and concurrent tobacco and cannabis users (n = 9,842) were identified. Risk factors for PJI and aseptic loosening at two-years were further quantified utilizing multivariable logistic regression analysis. Results: Compared to non-users, cannabis users experienced the highest odds for PJI and aseptic revisions, which were followed by concurrent cannabis and tobacco users and tobacco-only users. Concurrent users, as well as tobacco users were at higher risk for dislocation. Cannabis use was the most significant risk factor for PJI, followed by concurrent use and male sex. Conclusions: Our study found cannabis use to cause greater risk for superficial and deep infection. More research involving randomized trials are needed to fully elucidate the impact of cannabis use on shoulder arthroplasty procedures. Clinically, these findings can appropriately guide surgeons and patients alike regarding expectations prior to undergoing TSA. [ABSTRACT FROM AUTHOR]