Pro-p Groups Research Articles

Cyclic splittings of pro-p groups

In this paper, we prove a pro-p version of the Rips-Sela's Theorems on splittings of a group as an amalgamated free product or HNN-extension over an infinite cyclic subgroup.

The symbol length for elementary type pro-p groups and Massey products

For a prime number p and an integer m≥2, we prove that the symbol length of all elements of m-fold Massey products in H2(G,Fp), for pro-p groups G of elementary type, is bounded by (m2/4)+m. Assuming the Elementary Type Conjecture, this applies to all finitely generated maximal pro-p Galois groups G=GF(p) of fields F which contain a root of unity of order p. More generally, we provide such a uniform bound for the symbol length of all pullbacks ρ⁎(ω¯) of a given cohomology element ω¯∈Hn(G¯,Fp), where G¯ is a finite p-group, n≥2, and ρ:G→G¯ is a pro-p group homomorphism.

Cohomological properties of maximal pro-p Galois groups that are preserved under profinite completion

Abstract Let p be a prime number. One of the most difficult and important questions in Galois theory these days is determining which pro-p groups can occur as maximal pro-p Galois groups. Some restrictions of the structure of maximal pro-p Galois groups are already known, and therefore, the families of all pro-p groups satisfying these restrictions are in the center of the research. In the current paper we deal with three of these families: The family of all pro-p groups which satisfy hereditarily the n-vanishing Massey product property, the family of 1-cyclotomic oriented pro-p groups, and the family of pro-p groups that are hereditarily of p-absolute Galois type. We show that all these families are closed under taking profinite completion of each order.

Chasing Maximal Pro-p Galois Groups via 1-Cyclotomicity

Let p be a prime. We prove that certain amalgamated free pro-p products of Demushkin groups with pro-p-cyclic amalgam cannot give rise to a 1-cyclotomic oriented pro-p group, and thus do not occur as maximal pro-p Galois groups of fields containing a root of 1 of order p. We show that other cohomological obstructions which are used to detect pro-p groups that are not maximal pro-p Galois groups—the quadraticity of Z/pZ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {Z}/p\\mathbb {Z}$$\\end{document}-cohomology and the vanishing of Massey products—fail with the above pro-p groups. Finally, we prove that the Minač–Tân pro-p group cannot give rise to a 1-cyclotomic oriented pro-p group, and we conjecture that every 1-cyclotomic oriented pro-p group satisfy the strong n-Massey vanishing property for n=3,4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n=3,4$$\\end{document}.

Relatively projective pro-p groups

Relatively projective pro-p groups

Remimazolam's Effects on Postoperative Nausea and Vomiting Are Similar to Those of Propofol after Laparoscopic Gynecological Surgery: A Randomized Controlled Trial.

(1) Background: Remimazolam is a novel benzodiazepine that prevents postoperative nausea and vomiting (PONV), is more effective than volatile anesthetics, and was recently approved for use in Japan. (2) Methods: This prospective, double-blind, randomized controlled trial study aimed to compare the efficacy of remimazolam and propofol as general anesthetics in terms of the incidence of PONV after laparoscopic gynecological surgery (UMIN000046237). High-risk female patients who underwent general anesthesia with either remimazolam or propofol for the maintenance of anesthesia were enrolled. The primary outcome was the incidence of PONV in the two groups (i.e., REM versus PROP) 2 h and 24 h after surgery. The incidence of vomiting without nausea, rescue antiemetic use, and the severity of nausea were also evaluated. (3) Results: No significant differences in PONV were identified between the REM and PROP groups at 2 h or 24 h. Furthermore, no differences were observed in any of the measured parameters, and no adverse events were reported. (4) Conclusions: The results of the present study suggest that remimazolam may be as effective as propofol in preventing PONV; however, further investigation is necessary to identify possible differences between these two agents.

Zassenhaus and lower central filtrations of pro-p groups considered as modules

The goal of this paper is to study the action of groups on Zassenhaus and lower central filtrations of finitely generated pro-p groups. We shall focus on the semisimple case. Particular attention is given to finitely presented groups of cohomological dimension less than or equal to two.

Generalized Stallings' decomposition theorems for pro-p groups

Generalized Stallings' decomposition theorems for pro-p groups

Frattini-resistant direct products of pro-p groups

A pro-p group G is called strongly Frattini-resistant if the function H↦Φ(H), from the poset of all closed subgroups of G into itself, is a poset embedding. Frattini-resistant pro-p groups appear naturally in Galois theory. Indeed, every maximal pro-p Galois group over a field that contains a primitive pth root of unity (and also contains −1 if p=2) is strongly Frattini-resistant. Let G1 and G2 be non-trivial pro-p groups. We prove that G1×G2 is strongly Frattini-resistant if and only if one of the direct factors G1 or G2 is torsion-free abelian and the other one has the property that all of its closed subgroups have torsion-free abelianization. As a corollary we obtain a group theoretic proof of a result of Koenigsmann on maximal pro-p Galois groups that admit a non-trivial decomposition as a direct product. In addition, we give an example of a group that is not strongly Frattini-resistant, but has the property that its Frattini-function defines an order self-embedding of the poset of all topologically finitely generated subgroups.

Protective effects of propolis on ischemia-reperfusion injury in a rat testicular torsion and detorsion model.

The torsion model of testis in a rat was adopted for evaluation of possible effects of propolis (Prop) on ischemia-reperfusion (IS/REP) injury. The healthy male Wistar rats (totally 24 animals) were randomized into four groups (n = 6) and animals experienced bilateral testicular torsions as follows: In sham group just, laparotomy was performed and in IS group, animals experienced a 3 hr period testicular IS. In IS/REP group, a 3 hr period of IS followed by a 3 hr period of testicular REP for left testis and a one-week testicular REP for right testis were done. In this group animals were gavaged by 1.00 mL normal saline 1 hr before the onset of IS. In IS/REP/ Prop group, the same procedures for IS/REP animals were followed as well as gavage of 1.00 mL Prop extract solution 1 hr before the onset of IS. Analyses of biochemistry, histology, inflammatory biomarkers and sperm parameters were carried out. In IS/REP/Prop group, nitric oxide synthase malondialdehyde, myeloperoxidase and 8-hydroxy-2 deoxyguanine in IS/REP/Prop group were significantly decreased and, superoxide dismutase, total glutathione, glutathione peroxidase, glutathione reductase and glutathione S-transferase were significantly increased compared to the other animals. In IS/REP/Prop group, seminiferous tubules (with normal spermatogenesis) showed all stages of spermatogenic cells with plentiful spermatozoa. Tubular deterioration and atrophy and spermatogenic cell loss in were seen in a limited extent. The mean concentrations of Interleukin-1 beta and tumor necrosis factor alpha in IS/REP/Prop were significantly decreased. Sperm quality was significantly improved by Prop in IS/REP/Prop group. It was concluded that Prop could be supportive in diminishing IS/REP injury in testicular tissue exposed to ischemia.

Cardiopulmonary and propofol-sparing effects of dexmedetomidine in total intravenous anesthesia in cats undergoing ovariohysterectomy.

This study aimed to assess the effect of dexmedetomidine on the propofol-based anesthesia of cats subjected to ovariohysterectomy. Twenty-eight cats were randomly allocated to four groups (seven cats in each) and premedicated with either 5 µg/kg dexmedetomidine (groups Dex 1, Dex 3 and Dex 5) or 0.05 ml saline (Prop group) intramuscularly. After the induction of anesthesia with propofol, total intravenous anesthesia was initiated with 300 µg/kg/min propofol plus 3 ml/kg/h NaCl 0.9% (Prop), or 200 µg/kg/min propofol plus dexmedetomidine at the rates of 1 µg/kg/h (Dex 1), 3 µg/kg/h (Dex 3) or 5 µg/kg/h (Dex 5). Cardiorespiratory variables were assessed 5 mins after induction and every 10 mins thereafter, until the end of anesthesia. The propofol infusion rate was adjusted every 10 mins (± 50 µg/kg/min) to maintain anesthetic depth. The times to extubation, sternal recumbency, ambulation and total recovery were recorded. Pain scoring was performed 1, 2, 4, 8, 12 and 24 h after the end of anesthesia. Dexmedetomidine produced a propofol-sparing effect of 72.8%, 71.1% and 74.6% in the Dex 1, Dex 3 and Dex 5 groups, respectively. Cats in the Prop group maintained higher heart rate values than the other groups, and the mean arterial pressure remained higher in the Dex 3 and Dex 5 groups. Rescue intraoperative analgesia (fentanyl bolus) was most frequent in the Prop group. There was no significant difference in the time of extubation. Cats in the Dex 1 and Dex 3 groups had a faster anesthetic recovery, with shorter times to achieving sternal recumbency, regaining ambulation and reaching full recovery. Cats in the Dex 1 and Dex 5 groups presented the best recovery quality scores, with 4 (range 4-5) and 4 (range 3-5), respectively, while the Prop group scored 1 (range 1-3), the worst anesthetic recovery score among the groups. The use of dexmedetomidine as a total intravenous anesthesia adjuvant, especially at doses of 1 and 3 µg/kg/h, reduces propofol consumption and improves cardiorespiratory stability and intraoperative analgesia, while promoting a better and quicker recovery from anesthesia.

Groups of p-absolute Galois type that are not absolute Galois groups

Let p be a prime. We study pro-p groups of p-absolute Galois type, as defined by Lam–Liu–Sharifi–Wake–Wang. We prove that the pro-p completion of the right-angled Artin group associated to a chordal simplicial graph is of p-absolute Galois type, and moreover it satisfies a strong version of the Massey vanishing property. Also, we prove that Demushkin groups are of p-absolute Galois type, and that the free pro-p product — and, under certain conditions, the direct product — of two pro-p groups of p-absolute Galois type satisfying the Massey vanishing property, is again a pro-p group of p-absolute Galois type satisfying the Massey vanishing property. Consequently, there is a plethora of pro-p groups of p-absolute Galois type satisfying the Massey vanishing property that do not occur as absolute Galois groups.

On pro-p groups with quadratic cohomology

The main purpose of this article is to study pro-p groups with quadratic Fp-cohomology algebra, i.e. H•-quadratic pro-p groups. Prime examples of such groups are the maximal Galois pro-p groups of fields containing a primitive root of unity of order p.We show that the amalgamated free product and HNN-extension of H•-quadratic pro-p groups is H•-quadratic, under certain necessary conditions. Moreover, we introduce and investigate a new family of pro-p groups that yields many new examples of H•-quadratic groups: p-RAAGs. These examples generalise right angled Artin groups in the category of pro-p groups. Finally, we explore “Tits alternative behaviour” of H•-quadratic pro-p groups.

Effects of Propolis on Serum Biochemical Parameters in Azaserine Treated Rats

Azaserine (o-diazoacetyl-L-serine) is an antimetabolite obtained from streptomycetes cultures and is used experimentally to produce atypical acinar cell focus (AACF) in rat exocrine pancreas. Propolis is a resinous hive product with antioxidant, anticarcinogenic, antimicrobial and anti-inflammatory effects that bees collect from the plants around them. In this study, we aimed performed to investigate the effect of ethanol extract of propolis (EEP) on serum biochemical changes in azaserin induced pancreatic cancer in Wistar rats. For this purpose, male Wistar albino rats were randomly divided into 4 groups, 10 in each group. AzCt and AzProp group 2-week-old male rats were given azaserine (30 mg/kg bw) intraperitoneally (ip). Propolis (EEP) (oral 80 mg/lt) was added to the drinking water of Prop and AzProp group rats. For the first time in this study, the effects of propolis on rats with neoplastic structures formed by azaserine were investigated in terms of biochemical parameters (AST, ALP, ALT, BILD, BILT, CHOL, LDH, TRIG, UREA, TAS, TOS and OSI). According to this; AzProp group values were compared to AzCt group, respectively, AST, UREA, TOS and OSI, there is a statistically significant difference in terms of values. As a result, it was seen that the oxidative stress caused by azaserine-induced neoplastic structures decreased with the use of propolis and that propolis had a positive effect on the measured biochemical parameters.

The finitely generated Hausdorff spectra of a family of pro-p groups

Recently the first example of a family of pro-p groups, for p a prime, with full normal Hausdorff spectrum was constructed. In this paper we further investigate this family by computing their finitely generated Hausdorff spectrum with respect to each of the five standard filtration series: the p-power series, the iterated p-power series, the lower p-series, the Frattini series and the dimension subgroup series. Here the finitely generated Hausdorff spectra of these groups consist of infinitely many p-adic rational numbers, and their computation requires a rather technical approach. This result also gives further evidence to the non-existence of a finitely generated pro-p group with uncountable finitely generated Hausdorff spectrum.

Myocardial protection of propofol on apoptosis induced by anthracycline by PI3K/AKT/Bcl-2 pathway in rats.

BackgroundThe release of proinflammatory cytokines is inhibited by propofol, which could reduce oxidative stress and suggests that propofol could ameliorate the adverse effects of anthracyclines in myocardial cells as a promising cardioprotective agent. The aim of the study was to evaluate the protective effects of propofol on phosphatidylinositol 3 kinase/protein kinase B/B cell lymphoma 2 (PI3K/AKT/Bcl-2) pathway in cardiomyocyte apoptosis induced by doxorubicin [adriamycin (ADM)] of rat cardiomyocytes in vivo.MethodsThe 40 F344 female rats were randomly divided into 4 groups (n=10): treatment control, ADM, Propofol (Prop) and ADM + Prop group. Blood samples were taken as baseline, before the 4th administration of the agents and before humane death. The serum levels of malondialdehyde (MDA), an oxidant factor, were detected by the thiobarbituric acid method. Superoxide dismutase (SOD) levels were analyzed by xanthine oxidase, and those of cardiac troponin I (cTnI), atrial natriuretic peptide (ANP) and B-type natriuretic peptide (BNP) were analyzed by enzyme linked immunosorbent assay (ELISA). Apoptosis of cardiac myocytes was measured by flow cytometry. The expression levels of PI3K-110α and pAKT-Ser473 and Bcl-2 proteins in rat heart tissue were detected by western blot.ResultsApoptosis induced by ADM was significantly reduced by propofol. Compared with the ADM group, the serum levels of MDA, cTnI and BNP in the ADM + Prop group were significantly downregulated. In addition, the PI3K-110α and pAKT-Ser473 expressions in the ADM group were significantly higher than those in the ADM + Prop group, and the increases in Bcl-2 expression in the ADM + Prop group was statistically significant compared with the ADM group.ConclusionsWe identified that the PI3K/AKT/Bcl-2 axis is involved in the regulation of cardiomyocyte apoptosis induced by ADM in vivo. In addition, our results elucidated that propofol had a protective role in cardiomyocyte apoptosis induced by ADM by suppressing the PI3K/AKT/Bcl-2 pathway.

Homology torsion growth of finitely presented pro-p groups

We prove that torsion in the abelianizations of open normal subgroups in finitely presented pro-[Formula: see text] groups can grow arbitrarily fast. By way of contrast in [Formula: see text]-adic analytic groups the torsion growth is at most polynomial.

Effects of Minocycline on Cognitive Impairment, Hippocampal Inflammatory Response, and Hippocampal Alzheimer's Related Proteins in Aged Rats after Propofol Anesthesia.

The aim of this study was to evaluate the effect of minocycline preadministration on cognitive dysfunction, hippocampal inflammatory response, and hippocampal senile dementia-related proteins induced by propofol anesthesia in aged rats. Sixty male SD rats, aged 20 months and weighing 340-410 g, were randomly divided into three groups: normal saline (NC) group, propofol group (prop), and minocycline (M) group. Prop group rats were injected intraperitoneally with 100 mg/kg propofol. The rats in group M were injected intraperitoneally with 50 mg/kg minocycline 30 minutes before injection of 100 mg/kg propofol, and the rest were the same as prop group. The rats in NC group were received intraperitoneal injection of the same amount of normal saline. The results indicated that compared with group C, the expressions of GSK-3β, acetyl-NF-κB (Lys310), Tau, and Amlyoid-beta were upregulated, the levels of TNF-α, IL-1β, and IL-6 were increased, the escape incubation period was prolonged, and the exploration time was shortened in prop group, while the expression of GSK-3β, acetyl-NF-κB (Lys310), Tau, and Amlyoid-beta in minocycline group was downregulated, the levels of TNF-α, IL-1β, and IL-6 were decreased, the escape incubation period was shortened, and the exploration time was shortened. In conclusion, preadministration of minocycline can improve cognitive impairment induced by propofol anesthesia in aged rats, and its mechanism of action may be related to minocycline inhibiting hippocampal inflammatory reaction and downregulating the expression of GSK-3β, acetyl-NF-κB (Lys310), Tau, and Amlyoid-beta proteins in hippocampus.

Mild pro-[formula omitted] groups and the Koszulity conjectures

Let p be a prime, and Fp the field with p elements. We prove that if G is a mild pro-p group with quadratic Fp-cohomology algebra H•(G,Fp), then the algebras H•(G,Fp) and grFp[[G]] — the latter being induced by the quotients of consecutive terms of the p-Zassenhaus filtration of G — are both Koszul, and they are quadratically dual to each other. Consequently, if the maximal pro-p Galois group of a field is mild, then Positselski’s and Weigel’s Koszulity conjectures hold true for such a field.

Primitive ideals in rational, nilpotent Iwasawa algebras

Given a p-adic field K and a nilpotent uniform pro-p group G, we prove that all primitive ideals in the K-rational Iwasawa algebra KG are maximal, and can be reduced to a particular standard form. Setting L as the associated Zp-Lie algebra of G, our approach is to study the action of KG on a Dixmier module D(λ)ˆ over the affinoid envelope U(L)ˆK, and to prove that all primitive ideals can be reduced to annihilators of modules of this form.