Nil Groups Research Articles

Results on $\mathrm{K}_1$ of general quadratic groups

In the first part of this article we discuss the relative cases of Quillen-Suslin's local-global principle for the general quadratic (Bak's unitary) groups, and its applications for the (relative) stable and unstable $\mathrm{K}_1$-groups. The second part is dedicated to the graded version of the local-global principle for the general quadratic groups and its application to deduce a result for Bass' nil groups.

The Classification of Torsion-free TI-Groups

An abelian group [Formula: see text] is called a [Formula: see text]-group if every associative ring with the additive group [Formula: see text] is filial. The filiality of a ring [Formula: see text] means that the ring [Formula: see text] is associative and all ideals of any ideal of [Formula: see text] are ideals in [Formula: see text]. In this paper, torsion-free [Formula: see text]-groups are described up to the structure of associative nil groups. It is also proved that, for torsion-free abelian groups that are not associative nil, the condition [Formula: see text] implies the indecomposability and homogeneity. The paper contains constructions of [Formula: see text] such groups of any rank from 2 to[Formula: see text] which are pairwise non-isomorphic.

A note on Feigelstock's conjecture on the equivalence of the notions of nil and associative nil groups in the context of additive groups of rings of finite rank

In the class of torsion-free abelian groups of finite rank, Feigelstock's conjecture on the equivalence of the notions of nil and associative nil groups is reduced to indecomposable groups. Torsion-free abelian groups $A$ of rank two such that every associative ring on $A$ is commutative but there exists a~non-commutative ring with the additive group $A$, are classified. Moreover, several valuable results concerning rings on torsion-free abelian groups of rank two achieved by Beaumont, Wisner, Jackett, Aghdam and Najafizadeh are complemented and their proof are greatly simplified.$

Performance of spring wheat lines near-isogenic for the reduced-tillering ‘tin’ trait across a wide range of water-stress environment-types

Agronomically-important traits were studied in 19 genetically-diverse sets of spring wheat (Triticum aestivum L.) lines near-isogenic (NILs) for the tiller inhibition gene (tin) in contrasting water-stress environment-types (ETs) in the Australian grainbelt between 2010 and 2014. The combination of NILs and ETs generated a wide range of spike numbers (103 to 885 spikes/m2), grain numbers per m2 (GNO; 1400 to 22800 grains/m2), and grain yields (0.3 to 8.2t/ha). On average, the presence of tin significantly reduced spike numbers (319 vs. 381 spikes/m2), increased the numbers of grains/spike (30 vs. 27 grains/spike), and thousand grain weight (TGW; 38.4 vs. 36.9g) at maturity. Variation in final biomass and GNO each explained over 70% of the genotypic variation in grain yield. Differences in anthesis biomass explained 38% of the variation in grain yield. The marginal yield response to increases in GNO was slightly greater in the tin-containing lines while the response to increases in final biomass was greater in the non-tin lines (p≤0.016). The harvest index varied with changes in ET (p<0.001) only. The interaction between presence/absence of tin and environment-type was significant for grain yield, total biomass, spike number, grains/spike, and GNO. Grain yields were similar between NIL groups in the lower-yielding ETs (mean yield <2t/ha) whereas non-tin lines were higher-yielding in more favourable ETs (mean yield >2t/ha). The rate of the response in grain yield, total biomass, spike number, and GNO to changes in environmental conditions from ‘unfavourable’ to ‘favourable’ was significantly greater in the non-tin lines, i.e. tin-containing genotypes were less responsive or plastic. Reduced-tillering plasticity was associated with increased plasticity in numbers of grains/spike and, to a lesser extent, TGW. The tin lines produced more grains/spike in ETs averaging 28 to 33 grains/spike while NIL groups had similar grains/spike in ETs with lower means. A slightly greater marginal yield response to increases in GNO in tin lines indicated that greater plasticity in the number of grains/spike and TGW can compensate for reduced spike numbers. It is concluded that large variability in adaptation exists within the group of tin-containing genotypes providing opportunities for further selection to improve wheat performance in environments yielding less than 2t/ha. Further work on the analysis of GNO and yield determination in tin wheat should also consider changes in resource utilisation and hence competition between plants as mediated by planting arrangement.

Mesenchymal progenitor cells combined with pentosan polysulfate mediating disc regeneration at the time of microdiscectomy: a preliminary study in an ovine model

Following microdiscectomy, discs generally fail to undergo spontaneous regeneration and patients may experience chronic low-back pain and recurrent disc prolapse. In published studies, formulations of mesenchymal progenitor cells combined with pentosan polysulfate (MPCs+PPS) have been shown to regenerate disc tissue in animal models, suggesting that this approach may provide a useful adjunct to microdiscectomy. The goal of this preclinical laboratory study was to determine if the transplantation of MPCs+PPS, embedded in a gelatin/fibrin scaffold (SCAF), and transplanted into a defect created by microdiscectomy, could promote disc regeneration. A standardized microdiscectomy procedure was performed in 18 ovine lumbar discs. The subsequent disc defects were randomized to receive either no treatment (NIL), SCAF only, or the MPC+PPS formulation added to SCAF (MPCs+PPS+SCAF). Necropsies were undertaken 6 months postoperatively and the spines analyzed radiologically (radiography and MRI), biochemically, and histologically. No adverse events occurred throughout the duration of the study. The MPC+PPS+SCAF group had significantly less reduction in disc height compared with SCAF-only and NIL groups (p < 0.05 and p < 0.01, respectively). Magnetic resonance imaging Pfirrmann scores in the MPC+PPS+SCAF group were significantly lower than those in the SCAF group (p = 0.0213). The chaotropic solvent extractability of proteoglycans from the nucleus pulposus of MPC+PPS+SCAF-treated discs was significantly higher than that from the SCAF-only discs (p = 0.0312), and using gel exclusion chromatography, extracts from MPC+PPS+SCAF-treated discs also contained a higher percentage of proteoglycan aggregates than the extracts from both other groups. Analysis of the histological sections showed that 66% (p > 0.05) of the MPC+PPS+SCAF-treated discs exhibited less degeneration than the NIL or SCAF discs. These findings demonstrate the capacity of MPCs in combination with PPS, when embedded in a gelatin sponge and sealed with fibrin glue in a microdiscectomy defect, to restore disc height, disc morphology, and nucleus pulposus proteoglycan content.

On the extension problem and the nil groups of rings of finite global dimension

A vanishing result is obtained in respect of nil groups of rings of finite global dimension. Also a connection is established with the extension problem.

Regulation of intestinal morphology and GALT by pituitary hormones in the rat

Here, the effects of neurointermediate (NIL), anterior (AL), and total hypophysectomy (HYPOX) on ileal mucosa cells and gut-associated lymphoid tissue (GALT) are reported. Compared with the sham-operated (SHAM) rats, the villi height and goblet cells numbers were significantly decreased in all groups. Lamina propria area decreased in AL and HYPOX, but not in NIL animals. CD8(+) but not CD4(+) lymphocytes decreased in the HYPOX and NIL groups. Paneth cells did not change, while IgA cells, IgM cells, and secretory IgA were significantly decreased in all groups. NIL but not AL animals lost significant numbers of IgA cells and secretory IgA. In summary, pituitary hormones exert lobe-specific regulatory effects on the gut and on GALT.

Induction and Computation of Bass Nil Groups for Finite Groups

Let G be a finite group. We show that the Bass Nil-groups NKn(RG), n ∈ Z, are generated from the p-subgroups of G by induction, certain twistings maps depending on elements in the centralizers of the psubgroups, and the Verschiebung homomorphisms. As a consequence, the groups NKn(RG) are generated by induction from elementary subgroups. For NK0(ZG) we get an improved estimate of the torsion exponent.

Results From the ENESTnd Extension Study: Efficacy and Safety of Patients (pts) with Chronic Myeloid Leukemia in Chronic Phase (CML-CP), Treated with Nilotinib 400 Mg Twice Daily (BID) After Suboptimal Response (SoR) or Treatment Failure (TF) to Imatinib 400 Mg Once Daily (QD) or Nilotinib 300 Mg BID

Abstract 114 Background:In ENESTnd, nilotinib demonstrated superior efficacy vs imatinib in pts with newly diagnosed CML-CP, including a significantly reduced rate of progression to AP/BC on treatment and a lower rate of SoR/TF. Pts in ENESTnd with SoR/TF on nilotinib 300 mg BID or imatinib could discontinue core study and enter an extension study; entrance was not allowed for intolerance. Here, we report the efficacy and safety of 49 such pts. Methods: 31 pts initially randomized to imatinib 400 mg QD (IM group) and 18 pts to nilotinib 300 mg BID (NIL group) in ENESTnd discontinued due to SoR/TF and received nilotinib 400 mg BID in this study. Progression and deaths in the extension study and after discontinuation of extension treatment have been previously reported as progression events after discontinuation of core ENESTnd treatment and in the OS analysis of ENESTnd. Results: Median time on extension treatment was 6 months (mo) for both groups (range, IM 0.2–24; NIL 1–14); 35/49 pts (71%) remain on study. Median nilotinib dose during extension treatment was equal to planned dose (800 mg/day). In the IM group, 65% of pts escalated imatinib to 400 mg BID prior to extension; 12 pts (46%) not in CCyR at extension entry and 7 pts (23%) not in MMR achieved these responses on extension treatment (table). Of these responders, 7/12 pts (58%) who achieved CCyR and 4/7 pts (57%) who achieved MMR had escalated imatinib to 400 mg BID on core study. In the NIL group, 1 pt (17%) not in CCyR at extension entry and 5 pts (29%) not in MMR, achieved this response on extension treatment. Overall, 4 pts in the IM group progressed to AP/BC (2 on extension treatment, 1 within 1 mo and the other > 12 mo after discontinuation). All 4 pts discontinued core study for TF. Overall, 1 pt in the NIL group progressed to AP/BC (< 1 mo after discontinuation of extension treatment); pt discontinued core study for SoR. The safety of nilotinib 400 mg BID was similar to that in the core study. Grade 3/4 AEs and drug-related AEs leading to discontinuation were reported in 52% and 10% of pts in the IM group. Higher rates of AEs in the first few mo of starting nilotinib in pts previously treated with imatinib were not unexpected as common AEs occur early following initial exposure. In the NIL group, grade 3/4 AEs were reported in 28% of pts and no pt discontinued due to drug-related AEs. No deaths were reported on extension treatment or ≤ 28 days of discontinuation; 4 deaths occurred > 28 days after discontinuation of treatment: 3 were CML-related (2 and 1 deaths in the IM and NIL groups, respectively) and occurred 8–10 mo after discontinuation. Conclusions: Results confirm the efficacy of nilotinib 400 mg BID for pts with CML-CP who had SoR/TF on imatinib, even after imatinib dose escalation. These results suggest that nilotinib 400 mg BID may be efficacious in pts with CML-CP with SoR/TF on nilotinib 300 mg BID, although longer follow-up is required. Whereas dose escalation of imatinib may overcome OCT-1 transporter activity in pts with correspondingly low imatinib plasma levels, nilotinib is not a substrate for OCT-1. The modest (∼16%) increase in nilotinib systemic exposure by dose escalation from 300 to 400 mg BID may benefit some patients with SoR/TF, but requires further evaluation. Currently, dose escalation of nilotinib from 300 to 400 mg BID appears safe with no additional safety signals. The extension study is ongoing and additional follow-up will provide more information moving forward. [Display omitted] Disclosures:Hochhaus:Ariad: Consultancy, Honoraria, Research Funding; Bristol Myers Squibb: Consultancy, Honoraria, Research Funding; Novartis Pharmaceutical: Consultancy, Honoraria, Research Funding; Merck: Consultancy, Honoraria, Research Funding. Ossenkoppele:Bristol Myers Squibb: Consultancy, Honoraria; Novartis Pharmaceutical: Consultancy, Honoraria, Research Funding. Gattermann:Novartis: Honoraria, Research Funding. Hughes:Bristol Myers Squibb: Honoraria, Membership on an entity's Board of Directors or advisory committees, Research Funding; Ariad: Honoraria, Membership on an entity's Board of Directors or advisory committees; Novartis: Honoraria, Membership on an entity's Board of Directors or advisory committees, Research Funding. Saglio:Bristol-Myers Squibb: Consultancy, Speakers Bureau; Novartis Pharmaceutical: Consultancy, Speakers Bureau; Pfizer: Consultancy. Larson:Novartis Pharmaceuticals: Consultancy, Honoraria, Research Funding. Hoenekopp:Novartis Pharmaceutical: Employment, Equity Ownership. Gallagher:Novartis: Employment, Equity Ownership. Yu:Novartis: Employment, Equity Ownership. Blakesley:Novartis Pharmaceutical: Employment. Kantarjian:Pfizer: Research Funding; Novartis: Research Funding; Novartis: Consultancy; BMS: Research Funding.

Algebraic K-theory of virtually free groups

We provide a general procedure for computing the algebraic K-theory of finitely generated virtually free groups. The procedure describes these groups in terms of the algebraic K-theory of various finite subgroups and various Farrell Nil groups. We illustrate this process by carrying out the computation for several interesting classes of examples. The first two classes serve as a check on the method and show that our algorithm recovers results that already exist in the literature. The last two classes of examples yield new computations.

Algebraic K -theory over the infinite dihedral group: a controlled topology approach

We use controlled topology applied to the action of the infinite dihedral group on a partially compactified plane and deduce two consequences for algebraic K-theory. The first is that the family in the K-theoretic Farrell–Jones conjecture can be reduced to only those virtually cyclic groups that admit a surjection with finite kernel onto a cyclic group. The second is that the Waldhausen Nil groups for a group that maps epimorphically onto the infinite dihedral group can be computed in terms of the Farrell–Bass Nil groups of the index 2 subgroup that maps surjectively to the infinite cyclic group.

A PRELIMINARY STUDY FOR IDENTIFICATION OF CANDIDATE AFLP MARKERS FOR LEAF RUST RESISTANCE GENE LR13 BY USING NEAR- ISOGENIC LINES OF SPRING WHEAT CV. THATCHER

The aim of the present study was to detect candidate DNA markers for leaf rust resistance gene Lr13. The NIL groups were constructed from a set of near isogenic lines of wheat cv. Thatcher containing in total 41 different Lr resistance genes. A total number of 246 primer combinations in the NIL groups were screened for DNA polymorphism by using the AFLP method. Twenty-eight AFLP primer combinations yielded 33 polymorphic bands in Tc+Lr13 line. To confirm these polymorphic bands, 28 primer combinations were investigated in 41 Thatcher near isogenic lines. Six primer combinations amplified specific band products in Tc+Lr13. It was concluded that these AFLP markers can be linked to Lr13 gene and in further studies on Lr13 resistance gene, these six AFLP markers should be analyzed in near isogenic lines. Also, construction of the NIL groups can be useful in terms of time and cost of the molecular researches including Thatcher near isogenic lines.

On the vanishing of twisted nil groups

AbstractLet G be a finite group and [G] its integral group ring. We prove that the twisted nil groups N([G]) vanish for all i ≤ 1 for G a finite group of square-free order.

On higher nil groups of group rings

On higher nil groups of group rings

On the nil groups of Waldhausen nils

We study the nil groups in the algebraic K-theory of the group ring of a virtually cyclic group. We prove these vanish in low degrees and mention some consequences in case the Farrell–Jones Isomorphism conjecture is valid.

Sources of variation in studies of the early bactericidal activity of antituberculosis drugs.

The early bactericidal activity (EBA) of antituberculosis drugs can be measured as the daily fall in cfu counts of Mycobacterium tuberculosis in sputum, usually during the first 2 days of treatment. In studies of low potency drugs, it is necessary to compare the treated group of patients with a group who receives no chemotherapy (Nil group). Over the past 10 years, five Nil groups of between five and 13 patients have been studied in Cape Town and two Nil groups in Hong Kong. There was a suggestion of an increase in variation within the Cape Town groups, as shown by a regression of variance size against study date (P = 0.06), which could not be attributed to technical causes. It might indicate increasing host resistance in the Western Cape epidemic of tuberculosis. Since the weighted mean of all Nil groups at Cape Town was 0.00036, very close to zero, it would seem safe to test means of treated groups against zero thus increasing precision and avoiding ethical problems in delaying treatment. In contrast to Nil groups, the variation found in five groups who received 300 mg isoniazid daily (INH 300) was uniform and homoscedastic, possibly because the additional variation was caused mainly by individual differences in plasma isoniazid concentrations and patient body weights. The mean EBA in the INH 300 series was 0.575 with 95% confidence limits of 0.515 and 0.636.

Non-Abelian Nil Groups

An abelian group G is called a nil group if the only ring R with additive group R+ = G is the zero-ring, R2 = {0}. Similarly, a non-abelian group G is defined to be a nil group if the only distributive near-ring R with R+ = G is the zero-near-ring, R2 = {0}. Several results concerning nil groups are obtained, including conditions for a finitely generated group to be nil, and a description of the nil finitely generated torsion groups. It is shown that perfect groups are nil, but non-trivial one-relator groups are not nil. For certain groups G, a complete description of the distributive near-rings R with R+ = G is given.

Control and relaxation over the circle

Introduction and statement of results Moduli spaces of manifolds and maps Wrapping-up and unwrapping as simplicial maps Relaxation as a simplicial map The Whitehead spaces Torsion and a higher sum theorem Nil as a geometrically defined simplicial set Transfers Completion of the proof Comparison with the lower algebraic nil groups Appendix A. Controlled homotopies on mapping tori Bibliography.

Waldhausen’s Nil groups and continuously controlled K-theory

Let Γ = Γ1 ∗G Γ2 be the pushout of two groups Γi, i =1 ,2, over a common subgroup G ,a ndH be the double mapping cylinder of the corresponding diagram of classifying spaces BΓ1 ← BG → BΓ2 .D enote byξ the diagram I p ← H 1 → X = H, where p is the natural map onto the unit interval. We show that the � Nil groups which occur in Waldhausen's description of K∗(ZΓ) coincide with the continuously controlled groups � K cc ∗ (ξ), defined by Anderson and Munkholm. This also allows us to identify the continuously controlled groups � K cc ∗ (ξ + ) which are known to form a theory in the variable ξ, with the homology part in Waldhausen's description of K∗−1(ZΓ). A similar result is also obtained for HNN extensions. 1. Recollections. Let the group Γ be a pushout as in the abstract. By first passing to the corresponding pushout of integral group rings, next applying Theorem 1 of (8), and finally taking homotopy groups, we arrive at the following version of Waldhausen's result concerning K∗(ZΓ ).

Splitting obstructions and properties of objects in the Nil categories

We show that the objects of Bass-Farrell categories which represent 0 in the corresponding Nil groups are precisely those which are stably triangular. This extends to Waldhausen's Nil group of the amalgamated free product with index 2 factors. Application