Automorphisms of abelian group extensions

Let $1 \to N \to G \to H \to 1$ be an abelian extension. The purpose of this paper is to study the problem of extending automorphisms of $N$ and lifting automorphisms of $H$ to certain automorphisms of $G$.Comment: 11 page

Hyperbolic Unit Groups and Quaternion Algebras

We Classify the rational quadratic extensions K and the finite groups G for which the group ring R[G] of G over the ring R of integers of K has the property that the group of units of augmentation 1 of R[G] is hyperbolic. We also construct units in a non-split quaternion algebra over R.Comment: 15 pages, this work is part of the PHd. Thesis of the third author. The paper was accepted in Proceedings Mathematical Science

On the IYB-property in some solvable groups

A finite group G is called Involutive Yang-Baxter (IYB) if there exists a bijective 1-cocycle χ:G⟶M for some ZG -module M. It is known that every IYB-group is solvable, but it is still an open question whether the converse holds. A characterization of the IYB property by the existence of an ideal I in the augmentation ideal ωZG complementing the set 1−G leads to some speculation that there might be a connection with the isomorphism problem for ZG . In this paper we show that if N is a nilpotent group of class two and H is an IYB-group of order coprime to that of N, then N⋊H is IYB. The class of groups that can be obtained in that way (and hence are IYB) contains in particular Hertweck’s famous counterexample to the isomorphism conjecture as well as all of its subgroups. We then investigate what an IYB structure on Hertweck’s counterexample looks like concretely

Detailed dimethylacetal and fatty acid composition of rumen content from lambs fed lucerne or concentrate supplemented with soybean oil

Articles in International JournalsLipid metabolism in the rumen is responsible for the complex fatty acid profile of rumen outflow compared with the dietary fatty acid composition, contributing to the lipid profile of ruminant products. A method for the detailed dimethylacetal and fatty acid analysis of rumen contents was developed and applied to rumen content collected from lambs fed lucerne or concentrate based diets supplemented with soybean oil. The methodological approach developed consisted on a basic/ acid direct transesterification followed by thin-layer chromatography to isolate fatty acid methyl esters from dimethylacetal, oxo- fatty acid and fatty acid dimethylesters. The dimethylacetal composition was quite similar to the fatty acid composition, presenting even-, odd- and branched-chain structures. Total and individual odd- and branched-chain dimethylacetals were mostly affected by basal diet. The presence of 18:1 dimethylacetals indicates that biohydrogenation intermediates might be incorporated in structural microbial lipids. Moreover, medium-chain fatty acid dimethylesters were identified for the first time in the rumen content despite their concentration being relatively low. The fatty acids containing 18 carbon-chain lengths comprise the majority of the fatty acids present in the rumen content, most of them being biohydrogenation intermediates of 18:2n26 and 18:3n23. Additionally, three oxo- fatty acids were identified in rumen samples, and 16-O-18:0 might be produced during biohydrogenation of the 18:3n23

Incidence and predictors of hospital readmission in children presenting with severe anaemia in Uganda and Malawi: a secondary analysis of TRACT trial data

Background: Severe anaemia (haemoglobin < 6 g/dL) is a leading cause of recurrent hospitalisation in African children. We investigated predictors of readmission in children hospitalised with severe anaemia in the TRACT trial (ISRCTN84086586) in order to identify potential future interventions. Methods: Secondary analyses of the trial examined 3894 children from Uganda and Malawi surviving a hospital episode of severe anaemia. Predictors of all-cause readmission within 180 days of discharge were identified using multivariable regression with death as a competing risk. Groups of children with similar characteristics were identified using hierarchical clustering. Results: Of the 3894 survivors 682 (18%) were readmitted; 403 (10%) had ≥2 re-admissions over 180 days. Three main causes of readmission were identified: severe anaemia (n = 456), malaria (n = 252) and haemoglobinuria/dark urine syndrome (n = 165). Overall, factors increasing risk of readmission included HIV-infection (hazard ratio 2.48 (95% CI 1.63–3.78), p < 0.001); ≥2 hospital admissions in the preceding 12 months (1.44(1.19–1.74), p < 0.001); history of transfusion (1.48(1.13–1.93), p = 0.005); and missing ≥1 trial medication dose (proxy for care quality) (1.43 (1.21–1.69), p < 0.001). Children with uncomplicated severe anaemia (Hb 4-6 g/dL and no severity features), who never received a transfusion (per trial protocol) during the initial admission had a substantially lower risk of readmission (0.67(0.47–0.96), p = 0.04). Malaria (among children with no prior history of transfusion) (0.60(0.47–0.76), p < 0.001); younger-age (1.07 (1.03–1.10) per 1 year younger, p < 0.001) and known sickle cell disease (0.62(0.46–0.82), p = 0.001) also decreased risk of readmission. For anaemia re-admissions, gross splenomegaly and enlarged spleen increased risk by 1.73(1.23–2.44) and 1.46(1.18–1.82) respectively compared to no splenomegaly. Clustering identified four groups of children with readmission rates from 14 to 20%. The cluster with the highest readmission rate was characterised by very low haemoglobin (mean 3.6 g/dL). Sickle Cell Disease (SCD) predominated in two clusters associated with chronic repeated admissions or severe, acute presentations in largely undiagnosed SCD. The final cluster had high rates of malaria (78%), severity signs and very low platelet count, consistent with acute severe malaria. Conclusions: Younger age, HIV infection and history of previous hospital admissions predicted increased risk of readmission. However, no obvious clinical factors for intervention were identified. As missing medication doses was highly predictive, attention to care related factors may be important. Trial registration: ISRCTN ISRCTN84086586. Keywords: Severe anaemia, Readmissio

The associated graded ring of a group ring

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Polynomial functors

1. Introduction: If G is a group, Z(G) its integral group-ring and AG the augmentation ideal, then we can form the Abelian groups Pn(G)=AG/AGn+1 and Qn(G)=AGn/AGn+1. In (5) we have studied the structure of these Abelian groups which we called polynomial grouups. If C denotes the category of Abelian groups, then Pn and Qn are functors from C into C. We call these functors polynomial functors. The object of this work is to study the nature of these funtors. Except for n = 1, these functors are non-additive. In fact, in the sense of Eilenberg-Maclane (4) these are functors of degree exactly n (Theorem 2.3). Because of their non-additive nature, their derived functors cannot be calculated in the traditional Cartan-Eilenberg(1) method. We have to make use of the more recent theory of Dold-Puppe (3)

Dimension subgroups

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