Let G be a finite group. A subgroup H of G is called weakly H C − embedded in G if there exists a normal subgroup T of G such that H G = HT and H g ∩ N T ( H ) ≤ H for all g ∈ G , where H G is the normal closuer of H in G. A subgroup H of G has a supersolvable supplement in G if there exists a supersolvable subgroup K of G such that G = HK . In this paper, we investigate the structure of G under the assumption that certain subgroups of G of prime power orders either are weakly H C − embedded in G or have supersolvable supplements in G. Our results improved and generalized some recent results in the literature.

Hypertension management remains challenging due to coexisting insulin resistance (IR) and arterial stiffness-two silent yet synergistic drivers of atherosclerotic cardiovascular disease (ASCVD). This study aimed to evaluate their joint impact on ASCVD risk and assess their utility in predictive, preventive, and personalized strategies. In this prospective cohort study of 30,094 adults with hypertension, IR was assessed using the triglyceride-glucose (TyG) index (calculated as ln [TG (mg/dL) × FBG (mg/dL)/2]) and arterial stiffness via brachial-ankle pulse wave velocity (baPWV). Time-to-event analyses examined their individual and combined associations with ASCVD incidence. Over a median 5.6-year follow-up, 1655 ASCVD cases occurred. TyG exhibited a dose-response relationship with ASCVD across baPWV strata. Each 1-SD increase in TyG was associated with a higher ASCVD risk in the elevated baPWV subgroup (HR: 1.17, 95% CI: 1.07-1.27) than in the normal baPWV subgroup (HR: 1.11, 95% CI: 1.02-1.21). A significant additive interaction was observed: individuals with both elevated TyG and baPWV had the highest ASCVD risk (HR: 1.93, 95% CI: 1.66-2.25), with 33.4% of the joint risk attributable to their interaction. Adding both biomarkers to traditional models improved discrimination (C-index: 0.66 to 0.68) and reclassification (NRI: 18.63%, P < 0.001). This study reveals a synergistic effect of IR and arterial stiffness on ASCVD risk and provides strong support for their integration into predictive models. This dual-biomarker approach enables early identification of high-risk hypertensive phenotypes and aligns with the predictive, preventive, and personalized medicine (PPPM) paradigm to optimize cardiovascular outcomes through tailored intervention. The online version contains supplementary material available at 10.1007/s13167-025-00421-8.

Therapeutic potential of spiramycin-nanoparticles and Aluvia in experimental congenital toxoplasmosis.

Unipotent normal subgroups of algebraic groups

The combined latent syndesmotic diastasis (LSD) leads to longer rehabilitation time and poor outcomes for ankle sprains or chronic lateral ankle instability (CLAI) cases. Identifying LSD by imaging is challenging, especially for plain radiographs. This study aimed to determine the osseous ankle characteristics of CLAI combined with LSD on anteroposterior (AP) radiographs, as well as to provide a potential approach to detecting concomitant LSD. All CLAI patients receiving arthroscopic surgery in our hospital from August 2020 to August 2025 were retrospectively reviewed (CLAI group). Relative lateral malleolar length (RLML), relative medial malleolar length (RMML), and talocrural angle (TCA) were measured on the bilateral ankle weightbearing AP radiographs. The same parameters of 50 healthy ankle joints were measured on the weightbearing AP radiographs and compared with the CLAI group as a control group. The middle width of the syndesmotic space was measured under arthroscopy with the customized probe. With 3 mm as the threshold, the patients were then divided into the arthroscopic normal (AN) subgroup and the arthroscopic diastasis (AD) subgroup. These measurements were then compared between the AD and AN subgroup, as well as the injured and contralateral ankles, to explore the anatomical predisposition to LSD in CLAI patients. A total of 164 CLAI patients were included for analysis. No significant difference was observed in RLML, RMML, or TCA between the CLAI group and the control group. For both the AD and AN subgroups, there was no significant side-to-side difference in all parameters. The AD subgroup showed a significantly greater RLML (0.929 ± 0.052 vs 0.881 ± 0.076, P < .001) and TCA (14.1 ± 2.4 degrees vs 12.6 ± 2.4 degrees, P < .001) compared with the AN subgroup. The optimal cutoff value for RLML detecting LSD was0.911 (sensitivity, 72.9%; specificity, 66.4%). No radiographic osseous differences were observed between CLAI patients and the normal control group, nor were side-to-side differences detected, indicating the anatomy does not predispose to ankle sprain. In CLAI patients, greater RLML is associated with arthroscopically confirmed latent syndesmotic diastasis; furthermore, RLML may help identify patients who warrant closer evaluation for syndesmotic injury, but prospective studies are needed to determine whether RLML-guided arthroscopy improves management or outcomes. Level III, retrospective comparative study.

Abstract The Gluck–Wolf theorem and its general version [Navarro and Tiep, Annals of Math. 178 (2013), 1135–1171] relate arithmetic properties at a fixed prime of the ratios , for irreducible characters of a finite group that lie over a fixed ‐invariant irreducible character of a normal subgroup of , to the structure of Sylow ‐subgroups of . This result constituted a key step towards the recent proof [Malle et al., Annals of Math. 200 (2024), 557–608] of Brauer's Height Zero Conjecture. In this paper, we prove a further extension of the Gluck–Wolf theorem to sets of primes, with a mild condition on if the alternating group is involved in the group.

On $$c^{*}_p$$-normal subgroups of finite groups

Abstract Symmetries play an essential role in the construction and phenomenology of quantum field theories (QFTs). We discuss how to construct symmetries of QFTs by extending minimal “seed'' symmetry groups to larger groups that contain the seed(s) as subgroup(s). On the one hand, there are so-called “normal” extensions, which are given by outer automorphisms of the original symmetry group (including the trivial one) and contain the seed as a normal subgroup. On the other hand, there can be “unorthodox extensions” which do not have this property. We demonstrate our logic on the most general scalar potentials of the two- and three-Higgs-doublet models (2HDM and 3HDM). For the 2HDM, we show that all symmetry groups, including the different possible classes of CP and continuous symmetry groups, can be obtained from extensions of the smallest possible symmetry CP1 by consecutive outer automorphisms. Scanning over normal and unorthodox group extensions might be the easiest way to “machine learn” the possible symmetries of a QFT. However, many of the groups constructible in this way may not be realizable in a concrete model, in the sense that they lead to additional accidental symmetries. Hence, we also comment on a different, “top-down” way to obtain the possible realizable symmetry groups of a QFT based on the covariant transformation of couplings under the most general basis changes.

Abstract We give a new method for counting extensions of a number field asymptotically by discriminant, which we employ to prove many new cases of Malle’s Conjecture and counterexamples to Malle’s Conjecture. We consider families of extensions whose Galois closure is a fixed permutation group 𝐺. Our method relies on having asymptotic counts for 𝑇-extensions for some normal subgroup 𝑇 of 𝐺, uniform bounds for the number of such 𝑇-extensions, and possibly weak bounds on the asymptotic number of G / T G/T -extensions. However, we do not require that most 𝑇-extensions of a G / T G/T -extension are 𝐺-extensions. Our new results use 𝑇 either abelian or S 3 m S_{3}^{m} , though our framework is general.

The classification of the unitary irreducible representations of symmetry groups is a cornerstone of modern quantum physics, as it provides the fundamental building blocks for constructing the Hilbert spaces of theories admitting these symmetries. In the context of gravitational theories, several arguments point toward the existence of a universal symmetry group associated with corners, whose structure is the same for every diffeomorphism-invariant theory in any dimension. Recently, the representations of the maximal central extension of this group in the two-dimensional case have been classified using purely algebraic techniques. In this work, we present a complementary and independent derivation based on Kirillov’s orbit method. We study the coadjoint orbits of the group SL ( 2 , R ) ˜ ⋉ H 3 , where H 3 is the Heisenberg group of a quantum particle in one dimension. Our main result is that, despite the non-Abelian nature of the normal subgroup in the semidirect product, these orbits admit a simple description. In a coordinate system associated with modified Lie algebra generators, the orbits factorize into a product of coadjoint orbits of SL ( 2 , R ) and H 3 . The subsequent geometric quantization of these factorized orbits successfully reproduces the known representations.

Fuzzy group theory has evolved beyond single-valued memberships to account for dual polarity and uncertainty. Building on Dib’s fuzzy space and bipolar-valued fuzzy sets, we develop a unified algebraic theory of bipolar-valued fuzzy (BVF) subgroups, including BVF normal subgroups and BVF homomorphisms, via a BVF binary operation (BVFBO) on a BVF-space. We establish necessary and sufficient subgroup criteria, characterize normality through coset symmetry in BVF-space, and prove homomorphism properties that align BVF structures with their classical counterparts through correspondence theorems. The framework clarifies when associativity holds between subgroup elements and ambient BVF-group elements and provides constructive examples. This generalization resolves limitations tied to the absence of a bipolar fuzzy universal set and supports applications in polarity-sensitive decision systems and network analysis.

Introduction: N-terminal proBNP (NT-proBNP) is associated with morbidity and mortality in Heart Failure (HF), however it’s prognostic value in Atherosclerotic Renal Artery Stenosis (ARAS) is not established. Hypothesis: NT-proBNP will be associated with adverse outcomes and mortality in people with ARAS. Methods: The CORAL trial enrolled participants with ARAS and hypertension. NT-proBNP was measured using the Abbott Alinity i assay. We compared normal (NTproBNP&lt;125pg/mL) vs. elevated (NTproBNP≥125pg/mL) groups. NT-proBNP levels were also analyzed by quartiles. Outcomes were reported through 3 year follow up. The primary endpoint is a composite of death, myocardial infarction (MI), stroke, HF hospitalization, progression to end-stage renal disease or acute kidney injury event. Individual endpoints were also assessed. Results: 702 participants had plasma available for measurement of NT-proBNP. Median value for NT-proBNP was 331.1pg/mL with IQR of 163.4-718.2pg/mL. Using the established cutpoint of 125pg/mL for outpatients, 81% of patients had elevated NT-proBNP. Elevated NT-proBNP was associated with higher hazard of the composite endpoint(HR 2.1, 95% CI=1.45-3.03), death(HR 5.46, 95% CI=1.72-17.38) and HF hospitalization(HR 3.78, 95% CI=1.37-10.39). In quartile analysis, NTproBNP quartiles were as follows: Q1=11.2–161; Q2=162–330; Q3=331–723; Q4=724–21,211 pg/mL. Those in quartile 4 experienced the composite endpoint at a rate of 53.7% compared to 20% in quartile 1 ( p &lt;0.001). Those in quartile 4 had significantly higher hazard of the composite endpoint (HR 3.37, 95% CI=2.38-4.77), death (HR 11.45, 95% CI=4.08-32.14), HF hospitalization (HR 10.86, 95%CI=3.85-30.64) and progression to ESRD (HR 15.02, 95% CI=1.95-115.62) as compared to quartile 1. When comparing event rates between randomized treatments of medical therapy alone vs. stent plus medical therapy, composite endpoint rates between randomized groups were similar in the normal and elevated NT-proBNP subgroups. Conclusion: NT-proBNP is an effective biomarker for predicting adverse events in people with ARAS, but does not predict treatment response to stent intervention.

Race-related molecular differences in SLAMF7 expression drive disparities in multiple myeloma outcomes

Abstract We prove a Hurewicz‐type theorem for the dynamic asymptotic dimension originally introduced by Guentner, Willett, and Yu. Calculations of (or simply upper bounds on) this dimension are known to have implications related to cohomology of group actions and the ‐theory of their transformation group ‐algebras. Moreover, these implications are relevant to the current classification program for ‐algebras. As a corollary of our main theorem, we show that the dynamic asymptotic dimension of actions by groups on profinite completions along sequential filtrations by normal subgroups is often subadditive over extensions of groups, which shows that many such actions by elementary amenable groups are finite dimensional. We combine this extension theorem with other novel results relating the dynamic asymptotic dimension of such actions to the asymptotic dimension of corresponding box spaces. This allows us to give upper bounds on the asymptotic dimension of many box spaces (including those of infinitely many groups with exponential growth). For some of these examples, we can also find lower bounds by utilizing the theory of ends of groups.

Allogeneic Hematopoietic Stem Cell Transplantation Abrogates the Poor Prognosis of High-Risk Cytogenetics in Adult Philadelphia-Negative B-Cell Acute Lymphoblastic Leukemia.

This article serves as a continuation of our previous work 1, which remains our primary reference for investigating specific homological properties with completion. Let the rings not be necessarily commutative and the modules be the unitary left (resp. right) modules. Let (G, (Gn) N element of N) be a filtered normal group equipped with the group topology associated with the filtration (Gn)nEN formed of normal subgroups and C(G) the set of Cauchy sequences with values in G. We define an equivalence relation R on C(G) by: (xn)R(yn) (xn)-(yn)= (xn-yn) converges to 0, noted by (xn-yn) 0. The quotient set C(G)/R:+{(xn)| (xn)element of C(G)} denoted G is equipped with a group structure and is called the completed groupe of G. For any filtered ring (resp. left A-module) (A, (In)nelement ofN (resp.(M,(Mn)nelement of N), the completed group A (resp. M) is equipped with a ring structure (resp. A-module) by (an ) x (bn ) = (anbn ) (resp.(an).(mn)=(an.mn)) where (an), (bn) element of A(resp. (mn ) element of M) called completed ring (resp. module) of A (resp. M). And for all saturated multiplicative subset S of A that satisfies the left Ore conditions, S = {(xn) element of A ∣ (xn ) not-equal 0 and ∃ n0 element of N, n greater than or equal to n0,xn element of S} is a saturated multiplicative subset of A that satisfies the left Ore conditions 1. Among the main results of this article, we have : – the functors S-1 () is isomorphic toS-1(A) tensor product A−. and S-1 () is isomorphic to S-1(A) tensor productA−. – the functors Home A(S-1A tensor productAM,−) and HOM A(S-1Atensor productA M,−) are isomorphic. – the functors S-1Atensor productA – and HomA(S-1A,−) are adjoints. This Study Allows How Establish a Relationship Between Completion [2] and Localization [4] Under the Assumptions of a Topological Structure.

Objective: Allergic rhinitis (AR) continues to adversely affect the life quality of a substantial patient population, highlighting the necessity for enhanced treatment modalities. Our research utilized licorice extract (LE) in nasal irrigation for managing this condition, with its therapeutic efficacy gauged against traditional saline nasal irrigation (SNI) through clinical trials. Additionally, the study incorporated traditional Chinese medicine (TCM) principles, measuring not just subjective symptom relief but also the objective shifts in lung meridian electrical conductance (MEC), to provide a comprehensive evaluation of the treatment’s effectiveness. Methods: Based on our previous laboratory and animal studies, we developed an LE solution and applied it through nasal irrigation to treat AR. In a one-month controlled trial, 60 patients with AR received either licorice nasal irrigation (LNI) or SNI daily. We assessed treatment efficacy by subjective questionnaire scores (Total Nasal Symptom Score [TNSS] and 22-item Sino-Nasal Outcome Test [SNOT-22]) and objective lung MEC analysis. Result: In the trial, 30 participants were randomly allocated to each group, and 28 individuals in the LNI group and 24 in the SNI group finished the study without any side effects. The LNI group had better improvements in sneezing, nasal itchiness, and rhinorrhea, along with a greater overall TNSS reduction. On the SNOT-22, the LNI group scored better across most nasal and extra-nasal symptoms, sleep, and physiological and psychosocial well-being. Participants were sorted into low, normal, and high lung MEC subgroups. After treatment, those in the LNI group normalized their lung MEC levels in both the low and high subgroups, which was not observed in the SNI group. Conclusions: LNI markedly improves symptoms in patients with AR, enhancing their quality of life. This treatment method, integrating Western and TCM practices, also normalizes abnormal lung MEC values following therapy. It offers a method of objectively validating the effectiveness of treatments based on TCM theories.

This is a survey on what is known, up to date, on normal subgroups of Cremona groups. There are several different approaches to showing that they exist, and we will take a look at each of them, more or less in chronological order.

In this paper we consider Potts-SOS model, with spin values 0, 1, 2, on the Cayley tree of order two. We study the weakly periodic Gibbs measures for this model, with respect to normal subgroup of two index of the group representation of a Cayley tree.

Abstract Let 𝔼 be the HNN-extension of a group 𝐵 with subgroups 𝐻 and 𝐾 associated by an isomorphism φ : H → K \varphi\colon H\to K . Suppose that 𝐻 and 𝐾 are normal in 𝐵 and ( H ∩ K ) ⁢ φ = H ∩ K (H\cap K)\varphi=H\cap K . Under these assumptions, we prove necessary and sufficient conditions for 𝔼 to be residually a 𝒞-group, where 𝒞 is a class of groups closed under taking subgroups, quotient groups, and unrestricted wreath products. Among other things, these conditions give new facts on the residual finiteness and the residual 𝑝-finiteness of the group 𝔼.