Group Ring Research Articles

On twisted group ring isomorphism problem for p-groups

AbstractIn this article, we explore the problem of determining isomorphisms between the twisted complex group algebras of finite $p$ -groups. This problem bears similarity to the classical group algebra isomorphism problem and has been recently examined by Margolis-Schnabel. Our focus lies on a specific invariant, referred to as the generalized corank, which relates to the twisted complex group algebra isomorphism problem. We provide a solution for non-abelian $p$ -groups with generalized corank at most three.

Abnormalities of retinal function in type 2 diabetes mellitus patients without clinical diabetic retinopathy detected by multifocal electroretinogram

ObjectiveTo study the changes of retinal function in type 2 diabetes mellitus(DM) patients without apparently diabetic retinopathy via multifocal electroretinogram. Methods: Thirty-six type 2 DM patients (72 eyes) without visible diabetic retinopathy were selected as the experimental group, and thirty-five healthy subjects (70 eyes) were selected as the control group. All subjects were underwent multifocal electroretinogram (mf- ERG).ResultsCompared with the control group, the implicit time delay of the P1 wave in the first ring, third ring, fourth ring, and fifth ring of the experimental group was significant (t = -3.154, p = 0.004, t = -8.21, p = 0.000, t = -3.067, p = 0.004, t = -4.443, p = 0.000, respectively). The implicit time of the N1 wave in the fourth- and fifth-ring were also significantly delayed compared with the control group (t = -3.549, p = 0.001, t = 2.961, p = 0.005, respectively). Compared with the control group, the implicit time of the P1 wave and N1 wave in the temporal region of the experimental group were delayed (t = -2.148, p = 0.037, t = -2.834, p = 0.007, respectively). There were no significant difference between the experimental group and the control group of the temporal area in the amplitude density of P1 wave, N1 wave. There was no difference in the implicit time and amplitude density of the N1 and P1 waves in the nasal region between the experimental group and the control group. The multifocal electroretinogram complex parameters showed better specificity and sensitivity in the diagnosis of diabetic retinopathy.ConclusionThe multifocal electroretinogram can detect abnormal changes in the retina of type 2 DM patients without visible diabetic retinopathy. The multifocal electroretinogram complex parameter is a potential indicator for the early diagnosis of diabetic retinopathy.

Microvascular abnormalities induced by hand-transmitted vibration reflects in finger systolic blood pressure: a cross-sectional study in China.

Local vibration can cause microcirculatory abnormalities such as blood stasis and symmetrical intermittent digital artery vasospasm. Finger SBP (FSBP) measurement is a potential way of assessing vascular components. This study aims to comprehensively investigate the relationship between the occurrence of the vibration-induced white finger (VWF) and changes in FSBP and then set the application value of FSBP measurements in the early diagnosis of VWF. All samples were judgmental sampling from one factory. Totally 50 patients with VWF were the case group, while 50 without occupational hand-transmitted vibration exposure were the control group. FSBP measurements and epidemiological feature investigations were taken. There were significant reductions in FSBP level and %FSBP index at both 10 °C and 30 °C in fingers reported VWF ( P < 0.05). The %FSBP abnormal rate of the index, ring and little finger in the VWF group was higher than the control (44.00% vs. 18.00%, 78.00% vs. 26.00%, 64.00% vs. 8.00%). The %FSBP of the ring and little finger had a relatively high application value (area under curve = 0.902, 0.737), while their standard regression coefficients were -0.23 and -0.412. The diagnostic cutoff value of the ring finger was 77.60%, while the sensitivity and specificity were 86.67%. FSBP measurements were proven helpful in monitoring and diagnosing VWF prospectively and proved to have great application value in our study. %FSBP of the ring finger was the appropriate diagnostic index in FSBP measurements, while its abnormal value could be set as 80.00%.

Performance improvement on the cold flow properties of crude oil with high asphaltene by adjusting the polarity of the third monomer in polymers

AbstractAsphaltenes and waxes are the primary factors affecting the cold flow properties of crude oil. In this paper, based on the binary polymer of acrylate‐maleic anhydride (PM22‐MA), different third polar groups of acrylamide, N‐(hydroxymethyl) acrylamide, N‐phenylacrylamide (NPA), and styrene (SM) were introduced to synthesize a series of ternary pour point depressants (PPDs) to explore the effect of asphaltene on the cold flow properties of Xijiang (XJ) crude oil. Thereinto, PM22‐MA‐NPA containing amide group and benzene ring exhibited the best depressive effect, which decreased pour point by 14°C at 1500 ppm. The mechanism of interaction of the polar groups in PPDs with asphaltene was studied. The polar groups could form stronger hydrogen bonds with asphaltene, delaying the asphaltene macromolecule bonding, allowing the synergistic effect of PPDs and asphaltene to be better utilized to improve the cold flow properties of crude oil. Furthermore, the dipole moment magnitude and electron cloud density were calculated with Gaussian. It was found that the polar group with a dipole moment magnitude of 3.2244 debye and an electron cloud density ranging from −1.6364 to 1.9944 eV was the most suitable third polar monomer for the PPDs of XJ crude oil.

On the geometric fixed points of real topological cyclic homology

AbstractWe give a formula for the geometric fixed‐points spectrum of the real topological cyclic homology of a bounded below ring spectrum, as an equaliser of two maps between tensor products of modules over the norm. We then use this formula to carry out computations in the fundamental examples of spherical group rings, perfect ‐algebras and 2‐torsion‐free rings with perfect modulo 2 reduction. Our calculations agree with the normal L‐theory spectrum in the cases where the latter is known, as conjectured by Nikolaus.

Units, zero-divisors and idempotents in rings graded by torsion-free groups

Abstract The three famous problems concerning units, zero-divisors and idempotents in group rings of torsion-free groups, commonly attributed to Kaplansky, have been around for more than 60 years and still remain open in characteristic zero. In this article, we introduce the corresponding problems in the considerably more general context of arbitrary rings graded by torsion-free groups. For natural reasons, we will restrict our attention to rings without non-trivial homogeneous zero-divisors with respect to the given grading. We provide a partial solution to the extended problems by solving them for rings graded by unique product groups. We also show that the extended problems exhibit the same (potential) hierarchy as the classical problems for group rings. Furthermore, a ring which is graded by an arbitrary torsion-free group is shown to be indecomposable, and to have no non-trivial central zero-divisor and no non-homogeneous central unit. We also present generalizations of the classical group ring conjectures.

A Schur ring approach to supercharacters of groups associated with finite radical rings

We consider the central Schur ring associated with the standard supercharacters of the adjoint group G ( A ) of a finite radical ring A , and define supercharacters of the subgroup C G ( A ) ( σ ) consisting of elements fixed by an involution of G ( A ) naturally defined by an (anti-)involution of A . In particular, we extend known results for unipotent subgroups of the classical finite Chevalley groups.

New Binary Quantum Codes from Group Rings and Skew Group Rings

New Binary Quantum Codes from Group Rings and Skew Group Rings

Rhodium-catalyzed enantioselective in situ C(sp3)−H heteroarylation by a desymmetrization approach

A rhodium-catalyzed desymmetrization reaction for enantioselective methyl C−H arylation is achieved by utilizing an in situ arylating reagent via nucleophilic cyclization of o-aminoaryl alkyne. The reaction results in chiral indoles containing all-carbon quaternary stereocenters under atmospheric conditions, with a wide range of substrates exhibiting good enantioselectivity (44 examples). Mechnism and DFT studies show that the stereocontrol is reasonably achieved through the collaborative control of a large silicon substituted chiral ligand and C−H···π, LP···π interactions between aryl rings of the carboxylate group and the substrate. Control experiments demonstrate that Rh-aryl bond formation via in situ nucleophilic cyclization is more critical for reaction efficiency than via C−H activation of the nucleophilic cyclization byproduct.

Algebras of one-sided subshifts over arbitrary alphabets

We introduce two algebras associated with a subshift over an arbitrary alphabet. One is unital, and the other not necessarily. We focus on the unital case and describe a conjugacy between Ott–Tomforde–Willis subshifts in terms of a homeomorphism between the Stone duals of suitable Boolean algebras, and in terms of a diagonal-preserving isomorphism of the associated unital algebras. For this, we realise the unital algebra associated with a subshift as a groupoid algebra and a partial skew group ring.

Coherence for elementary amenable groups

We prove that for an elementary amenable group, coherence of the group, homological coherence of the group, and coherence of the integral group ring are all equivalent. This generalises a result of Bieri and Strebel for finitely generated soluble groups.

A note on one decomposition of the 2-primary part of K 2(ℤ[C p × (C 2) n

Let Cn be a cyclic group of order n. We investigate K 2 of integral group rings via the Mayer-Vietoris sequence, and give a decomposition of the 2-primary torsion subgroup of K 2 ( Z [ C p × ( C 2 ) n ] ) for any prime p ≡ 3 , 5 , 7 ( mod 8 ) , in particular, K 2 ( Z [ C 3 × ( C 2 ) n ] ) is proven to be a finite abelian 2-group. As an application, we prove K 2 ( Z [ C 3 × ( C 2 ) 2 ] ) is an elementary abelian 2-group of rank at least 14, at most 16.

Protein Cryoprotectant Ability of the Aqueous Zwitterionic Solution.

Protein cryopreservation is important for the long-term storage of unstable proteins. Recently, we found that N-acetylglucosaminyltransferase-V (GnT-V) can be cryopreserved in a deep freezer without temperature control using a dilute binary aqueous solution of 3-(1-(2-(2-methoxyethoxy)ethyl)imidazol-3-io)butane-1-carboxylate (OE2imC3C) [10 wt %, mole fraction of solute (x) = 7.75 × 10-3], an artificial zwitterion. However, it is unclear which solvent properties are required in these media to preserve unstable proteins, such as GnT-V. In this study, we investigated the melting phenomena and solution structure of dilute binary aqueous OE2imC3C solutions [x = 0-2.96 × 10-2 (0-30 wt %)] using differential scanning calorimetry (DSC) and Raman and Fourier transform infrared (FTIR) spectroscopies combined with molecular dynamics (MD) simulation to compare the cryoprotectant ability of OE2imC3C with two general cryoprotectants (CPAs), glycerol and dimethyl sulfoxide. DSC results indicated that aqueous OE2imC3C solutions can be melted at lower temperatures with less energy than the control CPA solution, with increasing x, primarily due to OE2imC3C having a higher content of unfrozen water molecules. Moreover, Raman and FTIR results showed that the high content of unfrozen water molecules in aqueous OE2imC3C solutions was due to the hydration around the ionic parts (the COO- group and imidazolium ring) and the OCH2CH2O segment. In addition, the MD simulation results showed that there were fewer structured water molecules around the OCH2CH2O segment than the hydration water molecules around the ionic parts. These solvent properties suggest that dilute aqueous OE2imC3C solutions are effective in preventing freezing, even in a deep freezer. Therefore, this medium has the potential to act as a novel cryoprotectant for proteins in biotechnology and biomedical fields.

An efficient ID-based cryptographic encryption based on group ring

For most of the traditional IBEs (identity-based encryptions), security totally relies on the safekeeping of private keys. In case the private key is exposed, all the previously generated ciphertext need to be reissued. Due to increased usage of unprotected devices or mobiles, the key exposure is frequent. Therefore, it is important to mitigate the threat originated due to the key exposure in case of IBE. To deal with this issue, in this paper, we construct a novel IBE based on group ring that also provides forward security. We show that the security of our novel IBE is based on the hardness of discrete logarithm problem in group ring. Moreover, against the chosen plaintext attack, we show that it is semantically secure in random oracle model. Finally, we compare our IBE with several other existing IBEs in terms of execution cost.

Assessment of functional changes in long‐standing type 1 diabetic patients without diabetic retinopathy with multifocal electroretinogram

Aims/Purpose: To early evaluate local functional changes in the retina of long‐standing type 1 diabetic patients (DM1) without diabetic retinopathy (DR) through the use of multifocal electroretinogram (mfERG).Methods: 46 eyes of 46 long‐standing DM1 patients without DR and 46 eyes of 46 healthy subjects were studied. Eyes with previous history of ocular diseases that could alter mfERG results were excluded. Participants were evaluated using mfERG with RETIscan recording system by Roland, following the standardized international guidelines of the International Society for Clinical Electrophysiology of Vision (ISCEV). The electrical density and implicit time of each first‐order response (K1) were measured and analysed in both study groups, as well as interocular differences.Results: Mean age was 48.00 ± 9.77 years in the DM1 group and 51.69 ± 4.75 years in the control group. The average duration of diabetes was 29.19 ± 7.85 years and the mean HbA1c level was 7.33 ± 0.9%. No statistically significant differences were found between the ages of the groups. In mfERG, a statistically significant decrease in P1 response density was recorded in the R1 ring (central 0°‐2°) in the DM1 group compared to the control subjects (p = 0.029). Additionally, the R1/R2 ratio was significantly lower in diabetic patients than in the control group (p = 0.009). There was also a statistically significant increase in the implicit time of P1 in the R5 ring (central &gt;15°) in the DM1 group compared to the control group (p = 0.027). No interocular differences were found in the DM1 group. Regarding quadrant analysis, no statistically significant differences were found in the DM1 group.Conclusions: In patients with long‐standing DM1 without RD, mfERG enables the detection of subclinical and local findings, which indicates the presence of a pre‐existing neurodegenerative process prior to the onset of retinal lesions.

Unit group of integral group ring ℤ(G × C3)

Presenting an explicit descryption of unit group in the integral group ring of a given non-abelian group is a classical and open problem. Let S3 be a symmetric group of order 6 and C3 be a cyclic group of order 3. In this study, we firstly explore the commensurability in unit group of integral group ring ℤ(S3 × C3) by showing the existence of a subgroup as (F55 ⋊ F3) ⋊ (S3∗× C2) where Fρ denotes a free group of rank ρ. Later, we introduce an explicit structure of the unit group in ℤ(S3 × C3) in terms of semi-direct product of torsion-free normal complement of S3 and the group of units in RS3 where R = ℤ[ω] is the complex integral domain since ω is the primitive 3rd root of unity. At the end, we give a general method that determines the structure of the unit group of ℤ(G × C3) for an arbitrary group G depends on torsion-free normal complement V (G) of G in U(ℤ(G × C3)) in an implicit form. As a consequence, a conjecture which is found in [21] is solved.

A secure key authentication scheme for cryptosystems based on DLP in group ring

A secure key authentication scheme for cryptosystems based on DLP in group ring

Combinatorial results implied by many zero divisors in a group ring

В работе Крута, Льва и Паха и последующей работе Элленберга и Гийсвейта было доказано, что для группы $G=G_0^n$, где $G_0\ne \{1,-1\}^m$ - фиксированная абелева группа и $n$ велико, любое множество $A\subset G$ без 3-прогрессий (т. е. таких троек $x$, $y$, $z$ различных элементов, что $xy=z^2$) содержит не больше чем $|G|^{1-c}$ элементов, где константа $c&gt;0$ зависит только от $G_0$. Если $G$, скажем, - большая циклическая группа, то это неверно. Цель настоящей работы - показать, что алгебраическое свойство группы, отвечающее этому различию, таково: в первом случае групповая алгебра $\mathbb{F}[G]$ над подходящим полем $\mathbb{F}$ содержит подпространство $X$ коразмерности не больше чем $|X|^{1-c}$, для которого $X^3=0$. Мы обсуждаем оценки, которые получаются для абелевых $p$-групп и некоторых матричных $p$-групп: группы Гейзенберга над $\mathbb{F}_p$ и унитреугольной группы над $\mathbb{F}_p$. Также мы показываем, как этот метод позволяет обобщить результаты о мультипликативных $k$-сочетаниях и о покрытии произведения множеств произведениями меньших множеств.

Crystal structure of 2-[(5-amino-1-tosyl-1H-pyrazol-3-yl)-oxy]-1-(4-meth-oxy-phen-yl)ethan-1-one 1,4-dioxane monosolvate.

In the structure of the title compound, C19H19N3O5S·C4H8O2, the two independent dioxane mol-ecules each display inversion symmetry. The pyrazole ring is approximately parallel to the aromatic ring of the oxy-ethanone group and approximately perpendicular to the tolyl ring of the sulfonyl substituent. An extensive system of classical and 'weak' hydrogen bonds connects the residues to form a layer structure parallel to (201), within which dimeric subunits are conspicuous; neighbouring layers are connected by classical hydrogen bonds to dioxanes and by 'weak' hydrogen bonds from Htol-yl donors.

Classification of irreducible based modules over the complex representation ring of $ S_4 $

&lt;abstract&gt;&lt;p&gt;The complex representation rings of finite groups are the fundamental class of fusion rings, categorified by the corresponding fusion categories of complex representations. The category of $ \mathbb{Z}_+ $-modules of finite rank over such a representation ring is also semisimple. In this paper, we classify the irreducible based modules of rank up to 5 over the complex representation ring $ r(S_4) $ of the symmetric group $ S_4 $. In total, 16 inequivalent irreducible based modules were obtained. In this process, the MATLAB program was used in order to obtain some representation matrices. Based on such a classification result, we further discuss the categorification of based modules over $ r(S_4) $ by module categories over the complex representation category $ {\rm Rep}(S_4) $ of $ S_4 $ arisen from projective representations of certain subgroups of $ S_4 $.&lt;/p&gt;&lt;/abstract&gt;