Pro-p Groups Research Articles

On tamely ramified pro-p-extensions over -extensions of

AbstractFor an odd prime number p and a finite set S of prime numbers congruent to 1 modulo p, we consider the Galois group of the maximal pro-p-extension unramified outside S over the ${\mathbb Z}_p$-extension of the rational number field. In this paper, we classify all S such that the Galois group is a metacyclic pro-p group.

SUBDIRECT PRODUCTS OF FREE PRO-p AND DEMUSHKIN GROUPS

We classify the pro-p subdirect products of type FPmof Demushkin or free pro-p groups, in both cases of non-trivial Euler characteristic.

The effects of propofol and dexmedetomidine infusion on fluid responsiveness in critically ill patients

BackgroundWe studied the effects of propofol or dexmedetomidine on preload dependency and fluid responsiveness in critically ill patients. MethodsIn the study, we included 91 patients with acute circulatory failure (70 ± 15 y) who received propofol (n = 45 patients, PROP group) or dexmedetomidine (n = 46 patients, DEX group). An initial passive leg-raising (PLR 1) test was performed in all patients to evaluate preload dependency at baseline. Propofol and dexmedetomidine were infused and titrated according to the Richmond Agitation Sedation Scale; the results ranged from −2 to −1, and the bispectral index values ranged from 60–75. A second PLR test (PLR 2) was performed before administration of a 250-mL normal saline fluid challenge over a 5-min period. We obtained central venous pressure and cardiac index (CI) measurements before and after the two PLR tests and volume expansion. An increase of ≥10% in CI during PLR was considered to be a positive test finding that was indicative of preload dependency, whereas an increase of <10% in CI during PLR was considered to be a negative test finding. ResultsAt baseline, 22 of 45 patients had negative PLR 1 in the PROP group, whereas 20 of 46 patients had negative PLR 1 in the DEX group. After propofol or dexmedetomidine sedation, there were significant decreases in CI (−9.5% [±6.6%] versus −16.4% [±8.5%], P < 0.001) in the PROP and DEX groups, respectively. In the PROP group, there were significant increases in CI (+18.4% [±9.5%] versus +10.7% [±12.3%], P < 0.05) induced by PLR 2 compared with that induced by PLR 1. In the DEX group, there were no significant increases in CI (+13.2% [±14.9%] versus +12.8% [±17.7%]) induced by PLR 2 compared with that induced by PLR 1. Although the mean arterial pressure values increased comparably with the volume expansion observed in both groups, the volume expansion resulted in a significantly higher increase in CI compared with the baseline values in the PROP group (3.2 ± 0.8 versus 3.2 ± 0.7 L/min/m2) but not in the DEX group (2.9 ± 0.7 versus 3.1 ± 0.8 L/min/m2, P < 0.05). ConclusionsWe observed that propofol infusion, but not dexmedetomidine infusion, can increase preload dependency and fluid responsiveness in patients with circulatory failure.

Galois module structure of local unit groups

We study the groups in the unit filtration of a finite abelian extension K of the field of p-adic numbers. We determine explicit generators of these groups as modules over the pro-p group ring of the Galois group of K over the p-adic numbers. We work in eigenspaces for powers of the Teichmueller character, first at the level of the field of norms for the extension of K by p-power roots of unity and then at the level of K.

The combined propranolol/TSST paradigm--a new method for psychoneuroendocrinology.

Upon perception of a stimulus as stressful, the human brain reacts with the activation of the hypothalamus-pituitary-adrenal (HPA) axis and the sympathetic nervous system (SNS), to mobilize energy resources to better cope with the stressor. Since the perception of the stressor is the initial stimulus, a synchronicity between the subjective perception of stress and the physiological stress reactivity should be expected. However, according to a recent meta-analysis, these associations are weak and inconsistent. The goal of the current study was to investigate the interaction between the SNS, HPA and subjective stress perceptions, by introducing an experimental manipulation of this interaction. For this purpose, we combined the SNS inhibitor propranolol with the Trier Social Stress Test, and measured endocrinological and psychological responses to the stressor. Thirty healthy male participants were recruited and randomly assigned to either a propranolol (PROP; n = 15) or placebo (PLC; n = 15) group. All subjects were administered 80 mg of propranolol 60 minutes prior to exposure to psychosocial stress. Salivary cortisol and alpha amylase (sAA), heart rate, blood pressure and subjective stress responses were assessed throughout the study. We observed significantly reduced sAA levels and heart rate increases in the PROP group in response to stress, with no effects of the drug on systolic or diastolic blood pressure changes. In line with previous studies, a significant increase in cortisol was seen in response to the stress exposure. Importantly, the cortisol increase was significantly higher in the PROP group. A typical increase in subjective stress could be seen in both groups, with no significant group differences emerging. Complementing previous work, this study further demonstrates a significant interaction between the HPA and the SNS during acute stress. The HPA activity was found to be elevated in the presence of a suppressed SNS in reactivity to the TSST.

Virtually free pro-p groups

We prove that in the category of pro-p groups any finitely generated group G with a free open subgroup splits either as an amalgamated free product or as an HNN-extension over a finite p-group. From this result we deduce that such a pro-p group is the pro-p completion of a fundamental group of a finite graph of finite p-groups.

Representation zeta functions of compact p-adic analytic groups and arithmetic groups

We introduce new methods from p-adic integration into the study of representation zeta functions associated to compact p-adic analytic groups and arithmetic groups. They allow us to establish that the representation zeta functions of generic members of families of p-adic analytic pro-p groups obtained from a global, “perfect” Lie lattice satisfy functional equations. In the case of “semisimple” compact p-adic analytic groups, we exhibit a link between the relevant p-adic integrals and a natural filtration of the locus of irregular elements in the associated semisimple Lie algebra, defined by the centralizer dimension. Based on this algebro-geometric description, we compute explicit formulas for the representation zeta functions of principal congruence subgroups of the groups SL3(o), where o is a compact discrete valuation ring of characteristic 0, and of the groups SU3(O,o), where O is an unramified quadratic extension of o. These formulas, combined with approximative Clifford theory, allow us to determine the abscissae of convergence of representation zeta functions associated to arithmetic subgroups of algebraic groups of type A2. Assuming a conjecture of Serre on the congruence subgroup problem, we thereby prove a conjecture of Larsen and Lubotzky on lattices in higher-rank semisimple groups for algebraic groups of type A2 defined over number fields.

Local Sylow theory of totally disconnected, locally compact groups

Abstract.We define a local Sylow subgroup of a totally disconnected, locally compact (t.d.l.c.) group

Carvedilol for primary prophylaxis of variceal bleeding in cirrhotic patients with haemodynamic non-response to propranolol

ObjectiveNon-selective β-blockers or endoscopic band ligation (EBL) are recommended for primary prophylaxis of variceal bleeding in patients with oesophageal varices. Additional α-adrenergic blockade (as by carvedilol) may increase the number...

Effects of propofol on ischemia-induced ventricular arrhythmias and mitochondrial ATP-sensitive potassium channels

To investigate the potential of propofol in suppressing ventricular arrhythmias and to examine whether mitochondrial ATP-sensitive potassium channels are involved. Male Sprague-Dawley rats were pretreated with intravenous infusion of propofol (Prop), a selective mitochondrial KATP channel inhibitor 5-hydroxydecanoate (5-HD), propofol plus 5-HD (Prop+5-HD), a potent mitochondrial K(ATP) channel opener diazoxide (DZ) or NS, respectively. The dosage of each drug was 10 mg/kg. The animals then underwent a 30 min-ligation of the left anterior descending artery. The severity of arrhythmias, the incidence of ventricular fibrillation (VF), and the time of the first run of ventricular arrhythmias were documented using an arrhythmia scoring system. Mitochondrial membrane potential (ΔΨm) was measured in freshly isolated rat cardiomyocytes with a fluorescence microscope. The arrhythmia scores in the Prop and DZ group were 2.6(0-5) and 2.4(0-5), respectively, which were significantly lower than that in the control group [4.9(2-8)]. VF was not observed in both Prop and DZ groups. The first run of ventricular arrhythmias was significantly postponed in the Prop group (10.5±2.2 vs 7.3±1.9 min). Bracketing of propofol with 5-HD eliminated the anti-arrhythmic effect of propofol. In isolated rat cardiomyocytes, propofol (50 μmol/L) significantly decreased ΔΨm, but when propofol was co-administered with 5-HD, the effect on ΔΨm was reversed. Propofol preconditioning suppresses ischemia-induced ventricular arrhythmias in the rat heart, which are proposed to be caused by opening of mitochondrial K(ATP) channels.

On tame pro-p Galois groups over basic $${\mathbb{Z}_p}$$ -extensions

For a prime number p and a finite set S of prime numbers congruent to 1 modulo p, we consider the Galois group of the maximal pro-p-extension unramified outside S over the \({\mathbb Z_p}\)-extension of the rational number field. In this paper, we give a family of S for which the Galois group is a metacyclic pro-p group with an application to Greenberg’s conjecture.

Superior recovery profiles of propofol-based regimen as compared to isoflurane-based regimen in patients undergoing craniotomy for primary brain tumor excision: a retrospective study

Studies comparing the recovery profiles of isoflurane- and propofol-based anesthesia for major intracranial surgery have reported contradictory results. The aim of our study was to clarify the emergence status in both regimens by investigating uniformly managed neuroanesthesia cases. The anesthesia database at Yamagata University Hospital covering the period 2002-2005 was retrospectively investigated for adult patients who underwent craniotomy for primary brain tumor excision. General anesthesia was provided by an isoflurane- (ISO group) or propofol-based (PROP group) regimen. Times to extubation and operating room (OR) discharge, perioperative consciousness levels, and perioperative variables were compared. Of the 202 surgeries performed during the study period, 77 and 82 patients were anesthetized with isoflurane and propofol, respectively. Demographic data were comparable between the two groups, although the American Society of Anesthesiology grade was worse in the PROP group. Extubation times [39.5 ± 14.6 min (ISO) vs. 29.5 ± 14.9 min (PROP); P < 0.001] and OR discharge times [67.2 ± 18.0 (ISO) vs. 53.9 ± 17.6 min (PROP); P < 0.001] were significantly shorter in the PROP, with significantly better immediate consciousness levels. The differences in levels of consciousness persisted for several hours postoperatively. PROP patients had significantly higher urine outputs and lower body temperatures during anesthesia. The incidences of shivering, nausea, vomiting, and convulsions were not significantly different between the groups. The time to discharge was similar between the groups. Propofol was associated with a better recovery profile and neurological condition than isoflurane, as indicated by shorter extubation and OR discharge times and better postoperative consciousness.

Bloch–Kato pro-p groups and locally powerful groups

Abstract. A Bloch–Kato pro-p group G is a pro-p group with the property that the 𝔽 p $\mathbb {F}_p$ -cohomology ring of every closed subgroup of G is quadratic. It is shown that either such a pro-p group G contains no closed free pro-p groups of infinite rank, or there exists an orientation θ : G → ℤ p × $\theta \colon G\rightarrow \mathbb {Z}_p^\times $ such that G is θ-abelian. In case that G is also finitely generated, this implies that G is powerful, p-adic analytic with d ( G ) = cd ( G ) $d(G)=\operatorname{cd}(G)$ , and its 𝔽 p $\mathbb {F}_p$ -cohomology ring is an exterior algebra. These results will be obtained by studying locally powerful groups. There are certain Galois-theoretical implications, since Bloch–Kato pro-p groups arise naturally as maximal pro-p quotients and pro-p Sylow subgroups of absolute Galois groups. Finally, we study certain closure operations of the class of Bloch–Kato pro-p groups, connected with the Elementary Type Conjecture.

Normal Zeta Functions of Some pro-p Groups

We give an explicit formula for the number of normal subgroups of index p n of the pro-p group , and for the normal zeta function associated with this group. Let 𝒬1(s, r) be the subgroups of the Nottingham group discovered by Ershov. We observe that these groups are isospectral with . This provides us with an infinite family of noncommensurable normally isospectral groups.

Free-by-finite pro-p groups and integral p-adic representations

Let F be a free pro-p group of finite rank n and \({C_{p^r}}\) a cyclic group of order pr. In this work we classify p-adic representations \({ C_{p^r}\longrightarrow GL_n(\mathbb{Z}_{p})}\) that can be obtained as a composite of an embedding \({C_{p^r}\longrightarrow {\rm Aut}(F)}\) with the natural epimorphism \({{\rm Aut}(F)\longrightarrow GL_n(\mathbb{Z}_{p})}\) .

Quotients of absolute Galois groups which determine the entire Galois cohomology

For a prime power q = p d and a field F containing a root of unity of order q we show that the Galois cohomology ring $${H^*(G_F,\mathbb{Z}/q)}$$ is determined by a quotient $${G_F^{[3]}}$$ of the absolute Galois group G F related to its descending q-central sequence. Conversely, we show that $${G_F^{[3]}}$$ is determined by the lower cohomology of G F . This is used to give new examples of pro-p groups which do not occur as absolute Galois groups of fields.

Baroreflex sensitivity is higher during acute psychological stress in healthy subjects under β-adrenergic blockade

Acute psychological stress challenges the cardiovascular system with an increase in BP (blood pressure), HR (heart rate) and reduced BRS (baroreflex sensitivity). β-adrenergic blockade enhances BRS during rest, but its effect on BRS during acute psychological stress is unknown. This study tested the hypothesis that BRS is higher during acute psychological stress in healthy subjects under β-adrenergic blockade. Twenty healthy novice male bungee jumpers were randomized and studied with (PROP, n=10) or without (CTRL, n=10) propranolol. BP and HR responses and BRS [cross-correlation time-domain (BRSTD) and cross-spectral frequency-domain (BRSFD) analysis] were evaluated from 30 min prior up to 2 h after the jump. HR, cardiac output and pulse pressure were lower in the PROP group throughout the study. Prior to the bungee jump, BRS was higher in the PROP group compared with the CTRL group [BRSTD: 28 (24–42) compared with 17 (16–28) ms·mmHg−1, P<0.05; BRSFD: 27 (20–34) compared with 14 (9–19) ms·mmHg−1, P<0.05; values are medians (interquartile range)]. BP declined after the jump in both groups, and post-jump BRS did not differ between the groups. In conclusion, during acute psychological stress, BRS is higher in healthy subjects treated with non-selective β-adrenergic blockade with significantly lower HR but comparable BP.

Myocardial Protection in Patients Undergoing Coronary Artery Bypass Grafting Surgery Using Minimized Extracorporeal Circulation in Combination With Volatile Anesthetic

The minimized extracorporeal circulation (ECC) is a safe alternative for coronary artery bypass grafting (CABG) and allows a reduction of the negative effects associated with conventional extracorporeal circulation. Experimental and clinical data indicate that the anesthetic regime might influence the ischemia-reperfusion injury in CABG surgery. The aim of our retrospective study was to investigate the cardioprotective effects of two different minimized ECC systems in combination with two different anesthetic concepts and to determine the impact on oxygen consumption during aortic cross-clamping (ACC). Data of 1,182 patients who underwent elective isolated CABG with minimized ECC from January 1, 2003, to December 31, 2008, were enrolled in a retrospective manner. Patients were allocated either to sevoflurane-based volatile anesthesia using PRECiSe system (SEVO group) or to propofol-based intravenous anesthesia using MECC system (PROP group). Postoperatively, the SEVO group showed lower concentrations of myocardial fraction of creatine kinase compared with the PROP group (p < 0.001). During the period of ACC, the values of systemic vascular resistance (SVR) were higher in SEVO group (p < 0.005). Also, the SEVO group showed lower oxygen consumption at each time point ACC (p < 0.0001). In conclusion, PRECiSe system using a microporous capillary oxygenator in combination with sevoflurane-based volatile anesthetic regimen seem to provide lower postoperative myocardial cell damage and to allow improved perfusion with higher SVRs and lower oxygen consumption during ACC.

Subgroups of finite index and the just infinite property

A residually finite (profinite) group G is just infinite if every non-trivial (closed) normal subgroup of G is of finite index. This paper considers the problem of determining which (closed) subgroups of finite index of a just infinite group are themselves just infinite. If G is just infinite and not virtually abelian, we show that G is hereditarily just infinite if and only if all maximal (closed) subgroups of finite index are just infinite. This result will be used to show that a finitely generated pro- p group G is just infinite if and only if G has no non-trivial finite normal subgroups and Φ ( G ) has a just infinite open subgroup.

Fully residually free pro-p groups

We prove that the pro- p completion of the orientable surface group of genus d is residually free pro- p if d is even or p = 2 . The case when p ≠ 2 , odd d > 1 is still open.