Green Correspondence for Virtually Pro-p Groups

Let p be prime, k a finite field of characteristic p, and G a virtually pro-p group. We prove an analogue of the Green Correspondence for finitely generated modules over the completed group algebra k[[G]].Comment: 7 pages. Based on material from author's PhD at Manchester Universit

Modular Representations of Profinite Groups

Our aim is to transfer several foundational results from the modular representation theory of finite groups to the wider context of profinite groups. We are thus interested in profinite modules over the completed group algebra k[[G]] of a profinite group G, where k is a finite field of characteristic p. We define the concept of relative projectivity for a profinite k[[G]]-module. We prove a characterization of finitely generated relatively projective modules analogous to the finite case with additions of interest to the profinite theory. We introduce vertices and sources for indecomposable finitely generated k[[G]]-modules and show that the expected conjugacy properties hold - for sources this requires additional assumptions. Finally we prove a direct analogue of Green's Indecomposability Theorem for finitely generated modules over a virtually pro-p group.Comment: 19 page

Brauer Theory for Profinite Groups

Brauer Theory for a finite group can be viewed as a method for comparing the representations of the group in characteristic 0 with those in prime characteristic. Here we generalize much of the machinery of Brauer theory to the setting of profinite groups. By regarding Grothendieck groups as functors we describe corresponding Grothendieck groups for profinite groups, and generalize the decomposition map, regarded as a natural transformation. We discuss characters and Brauer characters for profinite groups. We give a functorial description of the block theory of a profinite group. We finish with a method for computing the Cartan matrix of a finite group $G$ given the Cartan matrix for a quotient of $G$ by a normal $p$-subgroup.Comment: 16 page

The Influence of an Existentialist Philosophy Upon Theological Thought: Illustrated From the Works of Martin Heidegger and Rudolf Bultmann

Abstract Not Provided

An investigation of splanchnic blood flow in patients with colorectal cancer

Colorectal cancer is one of the most common forms of cancers worldwide and the second most common cause of cancer death in the European Union. Surgical resection of the tumour is the primary choice of treatment as it is the only option that offers a chance of permanent cure. However, approximately half the patients who undergo apparently curative surgery will die within five years. It has been shown that up to 30% of patients undergoing apparently curative surgery for colorectal cancer harbour occult liver metastases at the time of presentation and it is the presence of these hepatic metastases that determines the likelihood of death from disseminated disease. The liver possesses a dual blood supply, approximately 75% of the blood coming from the portal vein and 25% from the hepatic artery in the normal subject. There is evidence that these proportions are altered shortly after metastatic seeding in the liver. Previous investigations using Doppler ultrasonography have shown that hepatic arterial blood flow is increased in the presence of liver metastases, while some studies suggest that portal venous blood flow is reduced. The Doppler Perfusion Index (DPI), defined as the ratio of hepatic arterial to total liver blood flow, increases as a result of both these changes. An elevated DPI at the time of apparently curative surgery has been shown to be highly predictive of subsequent recurrence in the liver. It is not known, however, whether the DPI is the most effective index for quantifying the tumour-induced changes in liver blood flow. There is also only limited evidence on whether the primary colorectal tumour alters liver blood flow. To address these questions, hepatic arterial and portal venous blood flow were measured in a series of patients with colorectal liver metastases and normal control subjects. There was no significant difference in either component of liver blood flow between metastases patients with and without a primary or recurrent colorectal tumour. This confirms previous reports that the presence of a synchronous primary does not affect metastases driven blood flow changes. Hepatic arterial flow was increased in patients with liver metastases relative to controls, and portal venous flow was reduced. However, the latter difference was attributable to age mismatching, as portal venous blood flow was found to decline significantly with increasing age. An optimised index, the Dual Flow Index (DFI), was developed by logistic regression analysis to distinguish between metastases and control patients on the basis of the blood flow measurements. This was found to only marginally improve on the DPI in accuracy of discrimination (84% vs. 82% after age adjustment of blood flow). It was concluded that the DPI was close to optimal as a diagnostic index, but that the age-dependence of blood flow should be considered in clinical practice. Doppler ultrasonography is recognised to be an operator-dependent technique, and this may account for conflicting reports in the literature about the blood flow changes associated with liver metastases. It has been suggested that functional Computed Tomography (CT) may provide equivalent information about liver blood flow in a less operator-dependent manner. However, reports on the effectiveness of functional computed tomography in detecting liver metastases are conflicting. Dual-phase contrast-enhanced spiral CT scans were used to assess the varying parameters of tumour-induced changes in liver blood flow. Abdominal scans were performed in patients with liver metastases, colorectal cancer patients without overt metastatic disease, and patients with small benign hepatic haemangiomas. No significant differences were found between these patient groups after adjustment for age imbalances. It was concluded that too many variables affect CT parameters in the routine clinical scanning procedure employed in this and other reported studies for them to be useful for studying blood flow changes. Further work is required in this area using a disease-free normal control population, however Doppler ultrasound currently remains the method of choice for the non-invasive assessment of splanchnic blood flow. (Abstract shortened by ProQuest.)