Central Subgroup Research Articles

Set-direct factorizations of groups

We consider factorizations G=XY where G is a general group, X and Y are normal subsets of G and any g∈G has a unique representation g=xy with x∈X and y∈Y. This definition coincides with the customary and extensively studied definition of a direct product decomposition by subsets of a finite abelian group. Our main result states that a group G has such a factorization if and only if G is a central product of 〈X〉 and 〈Y〉 and the central subgroup 〈X〉∩〈Y〉 satisfies certain abelian factorization conditions. We analyze some special cases and give examples. In particular, simple groups have no non-trivial set-direct factorization.

Structure of the Eberlein compactification of locally compact Heisenberg type group $$\mathbb {Z}\times \mathbb {T} \times \mathbb {T}$$ Z × T × T

Given a locally compact group G, the Eberlein compactification\(G^{e}\) is the spectrum of the uniform closure of the Fourier–Stieltjes algebra B(G). Hence, it is the semigroup compactification related to the unitary representations of G. \(G^e\) is a semitopological semigroup compactification and thus a quotient of the weakly almost periodic compactification of G. In this paper we aim to study the Eberlein compactification of the group \(\mathbb {Z} \times \mathbb {T} \times \mathbb {T}\) equipped with Heisenberg type multiplication. First, we will see that transitivity properties of the action of \(\mathbb {Z} \times \mathbb {T}\) on the central subgroup \(\mathbb {T}\) force some aspects of the structure of \((\mathbb {Z} \times \mathbb {T} \times \mathbb {T})^{e}\) to be quite simple. On the other hand, we will observe that the Eberlein compactification of the direct product group \(\mathbb {Z} \times \mathbb {T}\) is large with a complicated structure, and can be realized as a quotient of the Eberlein compactification \((\mathbb {Z} \times \mathbb {T} \times \mathbb {T})^{e}\).

The Morita Theory of Quantum Graph Isomorphisms

We classify instances of quantum pseudo-telepathy in the graph isomorphism game, exploiting the recently discovered connection between quantum information and the theory of quantum automorphism groups. Specifically, we show that graphs quantum isomorphic to a given graph are in bijective correspondence with Morita equivalence classes of certain Frobenius algebras in the category of finite-dimensional representations of the quantum automorphism algebra of that graph. We show that such a Frobenius algebra may be constructed from a central type subgroup of the classical automorphism group, whose action on the graph has coisotropic vertex stabilisers. In particular, if the original graph has no quantum symmetries, quantum isomorphic graphs are classified by such subgroups. We show that all quantum isomorphic graph pairs corresponding to a well-known family of binary constraint systems arise from this group-theoretical construction. We use our classification to show that, of the small order vertex-transitive graphs with no quantum symmetry, none is quantum isomorphic to a non-isomorphic graph. We show that this is in fact asymptotically almost surely true of all graphs.

A first field report on Nachiring (Kiranti)

The Nachiring language belongs to the Kiranti branch of the Trans-Himalayan language family (a.k.a Tibeto-Burman or Sino-Tibetan) and is spoken in the Himalayan foothills of eastern Nepal. Within the Kiranti branch, Nachiring has been classified as belonging to the Khambu unit of the Central Kiranti subgroup, but no linguistic fieldwork has been undertaken so far and the language remains undocumented and undescribed. The present paper constitutes a first sociolingusitic survey of the Nachiring language, based on an initial field trip, and presents updates on the number of speakers, location, language usage and attitude, as well as a first linguistic inspection of the relationship between Nachiring and the closely related Kulung language. Nachiring is a highly endangered language and thus in severe need of linguistic documentation.

Quasitriangular structures of the double of a finite group

ABSTRACTWe give a classification of all quasitriangular structures and ribbon elements of 𝒟(G) explicitly in terms of group homomorphisms and central subgroups. This can equivalently be interpreted as an explicit description of all braidings with which the tensor category Rep(𝒟(G)) can be endowed. We also characterize their equivalence classes under the action of Aut(𝒟(G)) and determine when they are factorizable.

Significance of MYC/BCL2 Double Expression in Diffuse Large B-cell Lymphomas: A Single-center Observational Preliminary Study of 88 Cases

OBJECTIVES: To study the prevalence of MYC/BCL2 double expression in diffuselarge B-cell lymphomas (DLBCLs) and its prognostic value. MATERIAL AND METHODS: This is a retrospective observational study, which includespatients diagnosed with DLBCLs at King Chulalongkorn Memorial Hospital from 2013 to2014. The slides were reviewed, and MYC and BCL2 immunostains were scored accordingto Revised WHO 2016 Classification. Clinical data were collected from medical records.Patients were divided into two groups: double expression (DE) and non-double expression(NDE). Survivals and hazard ratios (HR) were calculated. RESULTS: Eighty-eight patients were included in the study and 40 (46%) had doubleexpression. The mean age was 60±16 years old; 40.9% were male and 59.1% werefemale. Eight patients were excluded from the survival analysis due to incompleteclinical data. Of the remaining 80 patients, there were 34 (42.5%) DE and 46 (57.5%)NDE. Median overall survival time (OS) and median progression-free survival time(PFS) tended to be lower in the DE group but was not statistically significant (Log-ranktest, p = 0.16). Multivariate analysis identified 4 confounders: sex, cell of origin (COO),risk group and addition of rituximab to the standard treatment. Adjusted HRs of the DEgroup were 1.21 (95%CI 0.63-2.31, p = 0.57) for OS and 1.20 (95%CI 0.63-2.30,p = 0.58) for PFS. In the germinal center subgroup (GCB) of DLBCL, patients with DEhad HRs of 4.33 (95%CI 0.80-23.37, p = 0.08, significance level of p < 0.10) for OS and4.61 (95%CI 0.80-23.37, p = 0.08) for PFS; but, these were not significant in the non-GCBsubgroup. CONCLUSION: MYC/BCL2 double expression (DE) is significantly associated withpoorer prognosis than non-double expression (NDE) among DLBCLs with GCBphenotype. MYC/BCL2 double expression should be reported in the pathologicaldiagnosis of DLBCLs. Keywords: MYC, BCL2, double expression, co-expression, diffuse large B-celllymphoma, prognosis.

Multipoint assessment of demarcation line depth after standard and accelerated cross-linking in central and inferior keratoconus

PurposeTo determine the changes in the depth of the demarcation line in the central to peripheral cornea following accelerated compared to standard corneal cross-linking (CXL). MethodsIn this prospective, non-randomized study, 60 eyes with progressive keratoconus underwent accelerated or standard CXL (30 in each group). Anterior segment optical coherence tomography (AS-OCT) was done one month later by two independent masked examiners to measure the depth of the demarcation line in the central cornea and on peripheral rings. ResultsThe inter-examiner agreement (intra-class correlation coefficient) was >0.75 for all measured points, and average measurements were used in the analysis. The depth of the visualized demarcation line in the center was 223.4 ± 67.4 μm and 354.9 ± 79.0 μm in the accelerated and standard groups, respectively (P < 0.001). The depth significantly decreased from the center to the 7 mm ring in both groups (all P < 0.05). This change was 7.7–26.1% and 2.2%–11.1% in the accelerated and standard groups, respectively. In the accelerated group, the demarcation line was deeper in the central cone sub-group compared to the inferior cone sub-group, but in the standard group, the demarcation line was deeper in the inferior cone sub-group (all P < 0.05). Cases with an inferior cone showed greater inter-group differences in all studied points. ConclusionsThe depth of the demarcation line with accelerated CXL is less than the standard protocol and decreases from the center towards the periphery. Demarcation lines are more homogenized with standard CXL. In cases with an inferior cone, demarcation line depth varies throughout the cornea.

Decreased adiponectin level in adults with central obesity and low 25-hydroxy vitamin D level

Background Vitamin D insufficiency is associated with obesity and central obesity, which is in turn associated with the accumulation of visceral fat. Visceral fat secretes adiponectin which has a role in the pathogenesis of the metabolic syndrome, diabetes mellitus and cerebrovascular disease. The aim of this study was to determine the relationship between serum 25-hydroxy vitamin D [25(OH)D] level and adiponectin level in adults with central obesity. Methods This study was a cross sectional study with 80 subjects with central obesity and 80 healthy subjects as controls. The age of the subjects ranged from 55 to 65 years. The data collection included anthropometry and blood biochemistry (lipid profile, fasting blood glucose, 25(OH)D, and adiponectin). The data were analyzed using independent t test with p &lt;0.05.Results Mean waist circumference and 25(OH)D level in the central obesity group were 94.9 ± 7.8 cm and 14.3 ± 6.6 ng/mL, respectively, and in the control group 72.4 ± 5.0 cm and 19.2 ± 8.6 ng/mL respectively. There were significant differences in adiponectin level between the central obesity group and the control group at the 25(OH)D level of &lt;20 ng/mL (p=0.001), but no significant differences between the two groups at the 25(OH)D level of ³20 ng/mL (p=0.538).Conclusion The central obesity subgroup with 25(OH)D level of &lt;20 ng/mL have lower adiponectin levels compared with the control group. This study demonstrates the role of adiponectin as a link between insulin resistance and vitamin D status in adults.

THE CENTRAL SUBGROUPS OF THE NONABELIAN TENSOR SQUARES OF SOME BIEBERBACH GROUPS WITH ELEMENTARY ABELIAN 2-GROUP POINT GROUP

Bieberbach groups are torsion free crystallographic groups. In this paper, our focus is on the Bieberbach groups with elementary abelian 2-group point group, The central subgroup of the nonabelian tensor square of a group is generated by for all in The purpose of this paper is to compute the central subgroups of the nonabelian tensor squares of two Bieberbach groups with elementary abelian 2-point group of dimension three.

Root class residuality of HNN-extensions with central cyclic associated subgroups

Let R be a root class of groups which is closed with respect to passage to quotient groups and contains at least one nonidentity group. A criterion for the R-residuality of an HNN-extension whose associated subgroups are cyclic and belong to the center of the base group is obtained.

Stable actions and central extensions

A probability-measure-preserving action of a countable group is called stable if its transformation-groupoid absorbs the ergodic hyperfinite equivalence relation of type II_1 under direct product. We show that for a countable group G and its central subgroup C, if G/C has a stable action, then so does G. Combining a previous result of the author, we obtain a characterization of a central extension having a stable action.

Generic irreducibilty of Laplace eigenspaces on certain compact Lie groups

If G is a compact Lie group endowed with a left invariant metric g, then G acts via pullback by isometries on each eigenspace of the associated Laplace operator \(\Delta _g\). We establish algebraic criteria for the existence of left invariant metrics g on G such that each eigenspace of \(\Delta _g\), regarded as the real vector space of the corresponding real eigenfunctions, is irreducible under the action of G. We prove that generic left invariant metrics on the Lie groups \(G={ SU}(2)\times \cdots \times { SU}(2)\times T\), where T is a (possibly trivial) torus, have the property just described. The same holds for quotients of such groups G by discrete central subgroups. In particular, it also holds for \({ SO}(3)\), \({ U}(2)\), \({ SO}(4)\).

Topology of unitary groups and the prime orders of binomial coefficients

Let $c:SU(n)\rightarrow PSU(n)=SU(n)/\mathbb{Z}_{n}$ be the quotient map of the special unitary group $SU(n)$ by its center subgroup $\mathbb{Z}_{n}$. We determine the induced homomorphism $c^{\ast}:$ $H^{\ast}(PSU(n))\rightarrow H^{\ast}(SU(n))$ on cohomologies by computing with the prime orders of binomial coefficients

Geochemical constraints on origin of hydrothermal volatiles from southern Tibet and the Himalayas: Understanding the degassing systems in the India-Asia continental subduction zone

Hydrothermal activities (e.g., hot springs and geysers) are extensively distributed in southern Tibet and the Himalayas, forming an east-west trending, ~2000-km-long, hydrothermal belt that represents the ongoing degassing systems in the India-Asia continental subduction zone (IACSZ). In this study, we report new data of chemical compositions and He-C-N isotopes for gas samples from representative hot springs in the hydrothermal belt, aimed at understanding volatile origin of the hydrothermal degassing systems in the IACSZ and their tectonic implications. According to spatial location, the samples are divided into western, central and eastern subgroups, which display spatially discernible geochemical characteristics, such as 3He/4He and CO2/3He ratios. The essential components required for volatile evolution include silicate rocks, carbonate rocks, sedimentary organic matter and a mantle-derived end-member, which are all expected in the IACSZ following a tectonic model incorporating an accretionary wedge and a magmatic front. On the basis of He-C-N isotope mixing calculations, together with constraints from petrogeochemical and geophysical studies, an enriched mantle wedge (EMW) is proposed as a potential candidate for the source of the mantle-derived components, which highlights the importance of recycled Indian continental materials compared to previous models that do not take this possibility for mantle source enrichment in account. The regional crustal rock assemblages composed of silicate rocks, carbonate rocks and sedimentary organic matter are interpreted as contaminants of the EMW-derived volatiles (as exemplified by degassing systems in the magmatic front) or as source materials of hydrothermal volatiles from degassing systems in the accretionary wedge. Following tectonic framework of the IACSZ, we suggest that spatial variations in volatile geochemistry (e.g., 3He/4He) are predominantly controlled by tectonic affinities (i.e., the accretionary wedge and magmatic front) of the hydrothermal degassing systems in southern Tibet and the Himalayas. The crustal-like 3He/4He ratios and high N2 and 4He contents agree well with the high sedimentary contributions to degassing systems in the accretionary wedge (including the Himalayas and fore-arc basins), whereas the high mantle-derived helium emissions in southern Tibet exhibit close affinities with contributions from the EMW-derived melts beneath the magmatic front. Moreover, regional fault systems with variable scales and depths of penetration would act as an extra factor that may perturb the across-IACSZ profile of 3He/4He ratios controlled by tectonic settings. Our interpretation on degassing systems in southern Tibet and the Himalayas may have the potential to provide constraints from volatile geochemistry for understanding material recycling mechanism and tectonic settings of the IACSZ.

The genetic characterization of an isolated remnant population of an endangered rodent (Cricetus cricetus L.) using comparative data: implications for conservation

Estimates of genetic diversity and phylogenetic affiliation represent an important resource for biodiversity assessment and a valuable guide to conservation and management. We have found a new population (Jawor—JW) of the common hamster Cricetus cricetus in western Poland that is remote from the nearest populations by 235–300 km. With the objective of genetically characterizing of this population, we compared it with other populations from Poland and Germany by taking into account sequences of four mitochondrial DNA genes and variation at 10 microsatellite loci. The JW population exhibited low levels of genetic diversity and allelic and haplotype richness, which likely reflects its extreme isolation. This factor, coupled with inbreeding and genetic drift, are major threats to JW. A neighbor-joining tree based on mtDNA haplotypes shows that JW clusters among samples representing the Central subgroup that is known from central Germany but that has not yet been identified in Poland. Findings presented here improve our understanding of the spread and diversification of the common hamster. We offer the following hypotheses to explain the observed pattern of mtDNA haplotype distribution: JW could be a byproduct of postglacial migrations or back-migrations from eastern refugia to the western part of Europe, or/and be a result of population and habitat fragmentation. We recommend translocation of individuals as an effective management strategy, both at the level of Central phylogeographic group and at the species level, to overcome the negative consequences of inbreeding and geographical isolation of the JW population.

Generalization of the Central Subgroup of the Nonabelian Tensor Square of a Crystallographic Group with Symmetric Point Group

The central subgroup of the nonabelian tensor square of a group denoted by is a crucial tool in exploring the properties of a group. It is a normal subgroup generated by the element for all In this paper, the central subgroup of the nonabelian tensor square of a crystallographic group with symmetric point group is constructed and generalized up to finite dimension.

Enlargement of deep medullary veins during the early clinical course of Sturge-Weber syndrome

Therapeutic improvements are required for primary CNS lymphoma (PCNSL) and secondary CNS lymphoma. PCNSLs are predominantly diffuse large B-cell lymphoma (DLBCL) classified in the non-germinal center (non-GC) subgroup.1 The role of B-cell receptor (BCR) signaling to continuously activate the NF-κB pathway is well-established in non-GC DLBCL.2 Mutations of MYD88 , CD79B , and TBL1XR1 , genes involved in the NF-κB pathway, are frequently encountered in PCNSL.3 Ibrutinib, an inhibitor of BCR signaling, led to an objective response rate of 50% in patients with relapsed or refractory systemic non-GC DLBCL.4 As a small molecule (MW = 440), with promising CNS distribution,5 ibrutinib represents a potential treatment for PCNSL. We report a retrospective case series of patients with relapsed and refractory CNS lymphoma treated with ibrutinib. Acknowledgment: The authors thank Cathie Germain, MA, and Cynthia Burnett, BA, for assistance with patient scheduling; Jane Cornett, RN, and Anne Deboard, RN, for performing sedation for imaging; Yang Xuan, BS, for MRI acquisition and preprocessing; and Michael Behen, PhD, for cognitive assessment of the patients .

Ibrutinib monotherapy in relapsed/refractory CNS lymphoma: A retrospective case series.

Therapeutic improvements are required for primary CNS lymphoma (PCNSL) and secondary CNS lymphoma. PCNSLs are predominantly diffuse large B-cell lymphoma (DLBCL) classified in the non-germinal center (non-GC) subgroup.1 The role of B-cell receptor (BCR) signaling to continuously activate the NF-κB pathway is well-established in non-GC DLBCL.2 Mutations of MYD88 , CD79B , and TBL1XR1 , genes involved in the NF-κB pathway, are frequently encountered in PCNSL.3 Ibrutinib, an inhibitor of BCR signaling, led to an objective response rate of 50% in patients with relapsed or refractory systemic non-GC DLBCL.4 As a small molecule (MW = 440), with promising CNS distribution,5 ibrutinib represents a potential treatment for PCNSL. We report a retrospective case series of patients with relapsed and refractory CNS lymphoma treated with ibrutinib.

Back to the roots: When diversity evokes increased group-based conventionalism

Previous research has demonstrated that emphasizing diversity within superordinate groups can either improve or impair subgroup relations. The present research investigated whether this can depend on the way in which diversity is activated. We activated diversity by presenting central or peripheral subgroups. We tested the effects on group-based conventionalism and subgroup attitudes within the superordinate group of “metal music fans”. Participants were members of the (majority) subgroup of death metal fans. When the superordinate group’s diversity was activated with peripheral subgroups, death metal fans showed higher group-based conventionalism than in the condition in which central subgroups were presented. Group-based conventionalism mediated the relation between diversity activation and subgroup attitudes. Higher group-based conventionalism led to less positive subgroup attitudes (Experiments 1 and 2). However, this detrimental “back to the roots”-process did only occur for majority members who perceived a high overlap of their subgroup and the superordinate group (Experiment 2). Underlying factors of this process and practical implications for multicultural contexts are discussed.

Rigid inner forms of real and p-adic groups

We dene a new cohomology set H 1 (u ! W;Z ! G) for an ane algebraic group G and a nite central subgroup, both dened over a local eld of characteristic zero, which is an enlargement of the usual rst Galois cohomology set of G. We show how this set can be used to give a precise conjectural description of the internal structure and endoscopic transfer of tempered L-packets for arbitrary connected reductive groups that extends the well-known conjectural description for quasi-split groups. In the case of real groups, we show that this description is correct using Shelstad’s work.