Hypercentral unit groups and the hyperbolicity of a modular group algebra

We classify groups G such that the unit group U-1 (ZG) is hypercentral. In the second part, we classify groups G whose modular group algebra has hyperbolic unit groups U-1 (KG).

Symplectic Representation of a Braid Group on 3-Sheeted Covers of the Riemann Sphere

We define Picard cycles on each smooth three-sheeted Galois cover C of the Riemann sphere. The moduli space of all these algebraic curves is a nice Shimura surface, namely a symmetric quotient of the projective plane uniformized by the complex two-dimensional unit ball. We show that all Picard cycles on C form a simple orbit of the Picard modular group of Eisenstein numbers. The proof uses a special surface classification in connection with the uniformization of a classical Picard-Fuchs system. It yields an explicit symplectic representation of the braid groups (coloured or not) of four strings.

Isomorphism of Commutative Modular Group Algebras

∗ The work was supported by the National Fund “Scientific researches” and by the Ministry of Education and Science in Bulgaria under contract MM 70/91.

Complex Hyperbolic Surfaces of Abelian Type

2000 Mathematics Subject Classification: 11G15, 11G18, 14H52, 14J25, 32L07.

FM127: Systemic metal ion levels in patients with modular neck total hip arthroplasties: a prospective cohort study

There is increasing evidence that modular neck stems are prone to corrosion-related complications. Recent studies showed elevated metal ions levels and occasional pseudotumor formation in patients with such implants. The purpose of this study was to compare systemic metal-ion levels in patients after primary THA with modular neck stems to those of patients after non-modular implants. To our knowledge, this is the first cohort study including a control group, THA without CoCr heads and dry-assembled neck-stem connections. Methods: 50 patients after THA at a minimum follow-up of 1 year have been selected for the study. Patients with multiple prosthesis or other implants have been deselected. All received a cementless SPS stem from Symbios (Ti6Al4V). 40 patients have the modular neck (CoCr) version and 10 a monobloc version. All bearings were either ceramic-ceramic or ceramic-polyethylene to minimize other sources of CoCr ion release. In the modular group, the neck was chosen pre-operatively based on a 3D planning, allowing for a dry assembly of the stem and neck on the back table before implantation. A plasma system coupled to mass spectrometry was used for a complete elementary quantification in blood and serum separately. Clinical outcome was measured using the Oxford Hip Score. Results : Complete data sets of 29 patients (24 in the modular neck-group (10male, mean age 63y, 35-84y) and 5 in the monobloc-group (3 male, 69 y, 51-83y) are available to date. Mean Co blood levels were .95 ug/L (.14-12.4) in the modular group vs .27 ug/L (.10-.73) in the monobloc group (p=.2). Respective values for Cr were significantly higher in the modular group (.99 g/L; range .75-1.21) compared to those in the monobloc group (.74 g/L ;.62-.86; p=.001). No significant difference was found when comparing serum levels. 5/24 patients had Co levels above 1 g/L (12/24 for Cr), which is by some considered as a relevant elevation. The maximum Co level was measured in an asymptomatic patient. The Oxford Hip Scores were similar in both groups. Conclusion: Cr levels were significantly elevated in the modular neck group compared to those in the monobloc group. 1/24 patients with a modular prosthesis exhibited Co levels, which are beyond the threshold accepted even for metal-on-metal bearing couples. These results have contributed to our decision to abandon the use of modular neck stems. Routine follow-up including annual measurements of systemic CoCr concentrations should be considered.

Sylow P-Subgroups of Abelian Group Rings

2000 Mathematics Subject Classification: Primary 20C07, 20K10, 20K20, 20K21; Secondary 16U60, 16S34.

Encryption methods using formal power series rings

Recently there has been a great deal of work on noncommutative algebraic cryptography. This involves the use of noncommutative algebraic objects as the platforms for encryption systems. Most of this work, such as the Anshel-Anshel-Goldfeld scheme, the Ko-Lee scheme and the Baumslag-Fine-Xu Modular group scheme use nonabelian groups as the basic algebraic object. Some of these encryption methods have been successful and some have been broken. It has been suggested that at this point further pure group theoretic research, with an eye towards cryptographic applications, is necessary.In the present study we attempt to extend the class of noncommutative algebraic objects to be used in cryptography. In particular we explore several different methods to use a formal power series ring R && x1; :::; xn && in noncommuting variables x1; :::; xn as a base to develop cryptosystems. Although R can be any ring we have in mind formal power series rings over the rationals Q. We use in particular a result of Magnus that a finitely generated free group F has a faithful representation in a quotient of the formal power series ring in noncommuting variables.

Über die Linearität der Teichmüllerschen Modulgruppe des Torus mit zwei Punktierungen

Über die Liniarität der Teichmüllerschen Modulgruppe des Torus mit zwei Punktierungen. In meiner Arbeit beschäftige ich mich mit Darstellungen der Teichmüllerschen Modulgruppe des Torus mit zwei Punktierungen. Mein Ansatz hierbei ist, die Teichmüllersche Modulgruppe in eine p-adische Liegruppe einzubetten. Sei nun F die von zwei Elementen erzeugte freie Gruppe und Aut(F) die Automorphismengruppe von F. Inhalt des ersten Kapitels ist es nun zu zeigen, daß folgende Aussagen äquivalent sind: - Die Teichmüllersche Modulgruppe des Torus mit zwei Punktierungen ist linear, - Aut(F)ist linear, - F besitzt eine p-Kongruenzstruktur, deren Folgen- glieder von Aut(F) festgehalten werden, also charak- teristisch sind. Im zweiten Kapitel wird unter anderem gezeigt, daß es eine Einbettung einer Untergruppe endlichen Indexes der Aut(F) in die Automorphismengruppe einer einfachen p-adischen Liegruppe gibt. Bisher ist unbekannt, ob die Buraudarstellung treu ist.In dieser Arbeit wird ein unendliches, lineares Gleichungssystem, dessen Lösungen gerade die Koeffizienten der Wörter des Kernes der Buraudarstellung sind, vorgestellt.Im dritten Kapitel wird mit den Methoden des 1.Kapitels gezeigt, daß der Torus mit zwei Punktierungen genau dann linear ist, wenn die Teichmüllersche Modulgruppe der Sphäre mit 5 Punktierungen es auch ist. Bekanntlich ist die 4. Braidgruppe linear. Nun ist aber die 4. Braidgruppe letztlich die Teichmüllersche Modulgruppe der abgeschlossenen Kreisscheibe mit 5 Punktierungen. Wenn man nun deren Randpunkte miteinander identifiziert und anschließend wegläßt, erhält man die 5-fach punktiereSphäre.Mit der eben beschriebenen Abbildung kann man zeigen, daß die Teichmüllersche Modulgruppe der fünffach punktierten Sphäre linear ist.

The M-theory origin of global properties of gauge theories

We show that global properties of gauge groups can be understood as geometric properties in M-theory. Different wrappings of a system of N M5-branes on a torus reduce to four-dimensional theories with AN−1 gauge algebra and different unitary groups. The classical properties of the wrappings determine the global properties of the gauge theories without the need to impose any quantum conditions. We count the inequivalent wrappings as they fall into orbits of the modular group of the torus, which correspond to the S-duality orbits of the gauge theories.

On realizability of p-groups as Galois groups

2000 Mathematics Subject Classification: 12F12, 15A66.

Nadel's Subschemes of Fano Manifolds X with a Picard Group Pic(X) Isomorphic to Z

∗The author supported by Contract NSFR MM 402/1994.

A modular distributed transactional memory framework

Dissertação para obtenção do Grau de Mestre em Engenharia Informática

The use of a modular titanium endoprosthesis in skeletal reconstructions after bone tumor resections: method presentation and analysis of 37 cases

We analyzed 37 patients who underwent segmental wide resection of bone tumors and reconstruction with a modular titanium endoprosthesis at the Orthopaedic Oncology Group, between 1992 and 1998. Twelve patients were male and 25 were female, with a mean age of 30 years (9 - 81). The mean follow-up was 14 months (2 - 48). The diagnoses were: osteosarcoma (14 cases), metastatic carcinoma (10), Ewing's sarcoma (4), giant cell tumor (4), malignant fibrous histiocytoma (3), chondrosarcoma (1), and aneurysmal bone cyst (1). Eleven articulated total knee, 8 partial proximal femur with bipolar acetabulum, 8 partial proximal humerus, 3 total femur, 2 partial proximal tibia, 2 diaphyseal femur, 2 diaphyseal humerus, and 1 total proximal femur with cementless acetabulum endoprosthesis implant procedures were done. The complications related to the procedure included: infection (5 cases), dislocation (3), module loosening (1), and ulnar nerve paresthesia (1). We used the following criteria for the clinical evaluation: presence of pain, range of motion, reconstruction stability, surgical and oncologic complications, and patient acceptance. The results were good in 56.8% of the cases, regular in 32.4% and poor in 10.8%.

An irreducibility criterion for group representations, with arithmetic applications

We prove a criterion for the irreducibility of an integral group representation p over the fraction field of a noetherian domain R in terms of suitably defined reductions of p at prime ideals of R. As applications, we give irreducibility results for universal deformations of residual representations, with a special attention to universal deformations of residual Galois representations associated with modular forms of weight at least 2.