On maximal subgroups of the multiplicative group of a division algebra

This note studies the question whether a multiplicative group of a division ring has a maximal subgroup. It is published in J. Algebra. This is a reputable journal in the subject algebra. Most of submitted papers from 5* schools in RAE was in this journal.

Maximal Subgroups of Compact Lie Groups

This report aims at giving a general overview on the classification of the maximal subgroups of compact Lie groups (not necessarily connected). In the first part, it is shown that these fall naturally into three types: (1) those of trivial type, which are simply defined as inverse images of maximal subgroups of the corresponding component group under the canonical projection and whose classification constitutes a problem in finite group theory, (2) those of normal type, whose connected one-component is a normal subgroup, and (3) those of normalizer type, which are the normalizers of their own connected one-component. It is also shown how to reduce the classification of maximal subgroups of the last two types to: (2) the classification of the finite maximal Sigma-invariant subgroups of centerfree connected compact simple Lie groups and (3) the classification of the Sigma-primitive subalgebras of compact simple Lie algebras, where Sigma is a subgroup of the corresponding outer automorphism group. In the second part, we explicitly compute the normalizers of the primitive subalgebras of the compact classical Lie algebras (in the corresponding classical groups), thus arriving at the complete classification of all (non-discrete) maximal subgroups of the compact classical Lie groups.

Finite groups and geometries: a view on the present state and on the future

The model: groups of Lie-Chevalley type and buildingsThis paper is not the presentation of a completed theory but rather a report on a search progressing as in the natural sciences in order to better understand the relationship between groups and incidence geometry, in some future sought-after theory Τ. The search is based on assumptions and on wishes some of which are time-dependent, variations being forced, in particular, by the search itself.A major historical reference for this subject is, needless to say, Klein's Erlangen Programme. Klein's views were raised to a powerful theory thanks to the geometric interpretation of the simple Lie groups due to Tits (see for instance), particularly his theory of buildings and of groups with a BN-pair (or Tits systems). Let us briefly recall some striking features of this.Let G be a group of Lie-Chevalley type of rank r, denned over GF(q), q = pn, p prime. Let Xr denote the Dynkin diagram of G. To these data corresponds a unique thick building B(G) of rank r over the Coxeter diagram Xr (assuming we forget arrows provided by the Dynkin diagram). It turns out that B(G) can be constructed in a uniform way for all G, from a fixed p-Sylow subgroup U of G, its normalizer NG(U) and the r maximal subgroups of G containing NG(U).

CLASSIFICATION OF SUBALGEBRAS OF THE CAYLEY ALGEBRA OVER A FINITE FIELD

We classify all unital subalgebras of the Cayley algebra O(q) over the finite field F(q), q = p(n). We obtain the number of subalgebras of each type and prove that all isomorphic subalgebras are conjugate with respect to the automorphism group of O(q). We also determine the structure of the Moufang loops associated with each subalgebra of O(q).

On Groups Whose Maximal Cyclic Subgroups Are Maximal

We consider the problem of classifying those groups whose maximal cyclic subgroups are maximal. We give a complete classification of those groups with this property and which are either soluble or residually finite.

Maximal compactness, min- imal Hausdor ness and reversibility of frames and a study on automorphism group of frames

One can do research in pointfree topology in two ways. The rst is the contravariant way where research is done in the category Frm but the ultimate objective is to obtain results in Loc. The other way is the covariant way to carry out research in the category Loc itself directly. According to Johnstone [23], \frame theory is lattice theory applied to topology whereas locale theory is topology itself". The most part of this thesis is written according to the rst view. In this thesis, we make an attempt to study about 1. the frame counterparts of maximal compactness, minimal Hausdor - ness and reversibility, 2. the automorphism groups of a nite frame and its relation with the subgroups of the permutation group on the generator set of the frame

Reduced maximal oxygen consumption and overproduction of proinflammatory cytokines in athletes

Objective: It was the aim of this study to evaluate whether chronic pain in athletes is related to performance, measured by the maximum oxygen consumption and production of hormones and cytokines. Methods: Fifty-five athletes with a mean age of 31.9 +/- 4.2 years engaged in regular competition and showing no symptoms of acute inflammation, particularly fever, were studied. They were divided into 2 subgroups according to the occurrence of pain. Plasma concentrations of adrenaline, noradrenaline, cortisol, prolactin, growth hormone and dopamine were measured by radioimmunoassay, and the production of the cytokines interleukin (IL)-1, IL-2, IL-4, IL-6, tumor necrosis factor-alpha, interferon-alpha and prostaglandin E-2 by whole-blood culture. Maximal oxygen consumption was determined during an incremental treadmill test. Results: There was no change in the concentration of stress hormones, but the athletes with chronic pain showed a reduction in maximum oxygen consumption (22%) and total consumption at the anaerobic threshold (25%), as well as increased cytokine production. Increases of 2.7-, 8.1-, 1.7- and 3.7-fold were observed for IL-1, IL-2, tumor necrosis factor-alpha and interferon-alpha, respectively. Conclusions: Our data show that athletes with chronic pain have enhanced production of proinflammatory cytokines and lipid mediators and reduced performance in the ergospirometric test. Copyright (c) 2008 S. Karger AG, Basel.

The classification and the conjugacy classes of the finite subgroups of the sphere braid groups

Let n >= 3. We classify the finite groups which are realised as subgroups of the sphere braid group B(n)(S(2)). Such groups must be of cohomological period 2 or 4. Depending on the value of n, we show that the following are the maximal finite subgroups of B(n)(S(2)): Z(2(n-1)); the dicyclic groups of order 4n and 4(n - 2); the binary tetrahedral group T*; the binary octahedral group O*; and the binary icosahedral group I(*). We give geometric as well as some explicit algebraic constructions of these groups in B(n)(S(2)) and determine the number of conjugacy classes of such finite subgroups. We also reprove Murasugi`s classification of the torsion elements of B(n)(S(2)) and explain how the finite subgroups of B(n)(S(2)) are related to this classification, as well as to the lower central and derived series of B(n)(S(2)).

Classification of the virtually cyclic subgroups of the pure braid groups of the projective plane

We classify the ( finite and infinite) virtually cyclic subgroups of the pure braid groups P(n)(RP(2)) of the projective plane. The maximal finite subgroups of P(n)(RP(2)) are isomorphic to the quaternion group of order 8 if n = 3, and to Z(4) if n >= 4. Further, for all n >= 3, the following groups are, up to isomorphism, the infinite virtually cyclic subgroups of P(n)(RP(2)): Z, Z(2) x Z and the amalgamated product Z(4)*(Z2)Z(4).

Algorithms for Finding Unitals and Maximal Arcs in Projective Planes of Order 16

The paper has been presented at the International Conference Pioneers of Bulgarian Mathematics, Dedicated to Nikola Obreshkoff and Lubomir Tschakalo ff , Sofia, July, 2006.

On Parabolic Subgroups and Hecke Algebras of some Fractal Groups

* The authors thank the “Swiss National Science Foundation” for its support.

Comparison between maximal lengthening and shortening contractions for biceps brachii muscle oxygenation and hemodynamics

Eccentric contractions (ECC) require lower systemic oxygen (O2) and induce greater symptoms of muscle damage than concentric contractions (CON); however, it is not known if local muscle oxygenation is lower in ECC than CON during and following exercise. This study compared between ECC and CON for changes in biceps brachii muscle oxygenation [tissue oxygenation index (TOI)] and hemodynamics [total hemoglobin volume (tHb) = oxygenated-Hb + deoxygenated-Hb], determined by near-infrared spectroscopy over 10 sets of 6 maximal contractions of the elbow flexors of 10 healthy subjects. This study also compared between ECC and CON for changes in TOI and tHb during a 10-s sustained and 30-repeated maximal isometric contraction (MVC) task measured immediately before and after and 1–3 days following exercise. The torque integral during ECC was greater (P < 0.05) than that during CON by ∼30%, and the decrease in TOI was smaller (P < 0.05) by ∼50% during ECC than CON. Increases in tHb during the relaxation phases were smaller (P < 0.05) by ∼100% for ECC than CON; however, the decreases in tHb during the contraction phases were not significantly different between sessions. These results suggest that ECC utilizes a lower muscle O2 relative to O2 supply compared with CON. Following exercise, greater (P < 0.05) decreases in MVC strength and increases in plasma creatine kinase activity and muscle soreness were evident 1–3 days after ECC than CON. Torque integral, TOI, and tHb during the sustained and repeated MVC tasks decreased (P < 0.01) only after ECC, suggesting that muscle O2 demand relative to O2 supply during the isometric tasks was decreased after ECC. This could mainly be due to a lower maximal muscle mass activated as a consequence of muscle damage; however, an increase in O2 supply due to microcirculation dysfunction and/or inflammatory vasodilatory responses after ECC is recognized.

Systemic inflammatory responses to maximal versus submaximal lengthening contractions of the elbow flexors

We compared changes in markers of muscle damage and systemic inflammation after submaximal and maximal lengthening muscle contractions of the elbow flexors. Using a cross-over design, 10 healthy young men not involved in resistance training completed a submaximal trial (10 sets of 60 lengthening contractions at 10% maximum isometric strength, 1 min rest between sets), followed by a maximal trial (10 sets of three lengthening contractions at 100% maximum isometric strength, 3 min rest between sets). Lengthening contractions were performed on an isokinetic dynamometer. Opposite arms were used for the submaximal and maximal trials, and the trials were separated by a minimum of two weeks. Blood was sampled before, immediately after, 1 h, 3 h, and 1-4 d after each trial. Total leukocyte and neutrophil numbers, and the serum concentration of soluble tumor necrosis factor-alpha receptor 1 were elevated after both trials (P < 0.01), but there were no differences between the trials. Serum IL-6 concentration was elevated 3 h after the submaximal contractions (P < 0.01). The concentrations of serum tumor necrosis factor-alpha, IL-1 receptor antagonist, IL-10, granulocyte-colony stimulating factor and plasma C-reactive protein remained unchanged following both trials. Maximum isometric strength and range of motion decreased significantly (P < 0.001) after both trials, and were lower from 1-4 days after the maximal contractions compared to the submaximal contractions. Plasma myoglobin concentration and creatine kinase activity, muscle soreness and upper arm circumference all increased after both trials (P < 0.01), but were not significantly different between the trials. Therefore, there were no differences in markers of systemic inflammation, despite evidence of greater muscle damage following maximal versus submaximal lengthening contractions of the elbow flexors.

Use of Bayesian MUNE to show differing rate of loss of motor units in subgroups of ALS

Objectives To evaluate differences among patients with different clinical features of ALS, we used our Bayesian method of motor unit number estimation (MUNE). Methods We performed serial MUNE studies on 42 subjects who fulfilled the diagnostic criteria for ALS during the course of their illness. Subjects were classified into three subgroups according to whether they had typical ALS (with upper and lower motor neurone signs) or had predominantly upper motor neurone weakness with only minor LMN signs, or predominantly lower motor neurone weakness with only minor UMN signs. In all subjects we calculated the half life of MUs, defined as the expected time for the number of MUs to halve, in one or more of the abductor digiti minimi (ADM), abductor pollicis brevis (APB) and extensor digitorum brevis (EDB) muscles. Results The mean half life of MUs was less in subjects who had typical ALS with both upper and lower motor neurone signs than in those with predominantly upper motor neurone weakness or predominantly lower motor neurone weakness. In 18 subjects we analysed the estimated size of the MUs and demonstrated the appearance of large MUs in subjects with upper or lower motor neurone predominant weakness. We found that the appearance of large MUs was correlated with the half life of MUs. Conclusions Patients with different clinical features of ALS have different rates of loss and different sizes of MUs. Significance: These findings could indicate differences in disease pathogenesis.

Maximal structuring of acyclic process models

This article addresses the transformation of a process model with an arbitrary topology into an equivalent structured process model. In particular, this article studies the subclass of process models that have no equivalent well-structured representation but which, nevertheless, can be partially structured into their maximally-structured representation. The transformations are performed under a behavioral equivalence notion that preserves the observed concurrency of tasks in equivalent process models. The article gives a full characterization of the subclass of acyclic process models that have no equivalent well-structured representation, but do have an equivalent maximally-structured one, as well as proposes a complete structuring method. Together with our previous results, this article completes the solution of the process model structuring problem for the class of acyclic process models.