Class two p groups as fixed point free automorphism groups

Suppose that AG is a solvable group with normal subgroup G where (|A|, |G|) = 1. Assume that A is a class two odd p group all of whose irreducible representations are isomorphic to subgroups of extra special p groups. If p^c ≠ r^d + 1 for any c = 1, 2 and any prime r where r^2d+1 divides |G| and if C_G(A) = 1 then the Fitting length of G is bounded by the power of p dividing |A|.

The theorem is proved by applying a fixed point theorem to a reduction of the Fitting series of G. The fixed point theorem is proved by reducing a minimal counter example. IF R is an extra spec r subgroup of G fixed by A₁, a subgroup of A, where A₁ centralizes D(R), then all irreducible characters of A₁R which are nontrivial on Z(R) are computed. All nonlinear characters of a class two p group are computed.

On automorphisms of finite abelian p-groups

Let A be a finitely generated abelian group. We describe the automorphism group Aut(A) using the rank of A and its torsion part p-part A(p). For a finite abelian p-group A of type (k(1),..., k(n)), simple necessary and sufficient conditions for an n x n-matrix over integers to be associated with an automorphism of A are presented. Then, the automorphism group Aut(A) for a finite p-group A of type (k(1), k(2)) is analyzed. (C) 2008 Mathematical Institute Slovak Academy of Sciences.

Free actions of abelian p-groups on the n-torus

In this work we make some contributions to the theory of actions of abelian p-groups on the n-Torus T-n. Set congruent to Z(pk1)(h1) x Z(pk2)(h2) x...x Z(pkr)(hr), r >= 1, k(1) >= k(2) >=...>= k(r) >= 1, p prime. Suppose that the group H acts freely on T-n and the induced representation on pi(1)(T-n) congruent to Z(n) is faithful and has first Betti number b. We show that the numbers n, p, b, k(i) and h(i) (i = 1,..,r) satisfy some relation. In particular, when H congruent to Z(p)(h), the minimum value of n is phi(p) + b when b >= 1. Also when H congruent to Z(pk1) x Z(p) the minimum value of n is phi(p(k1)) + p - 1 + b for b >= 1. Here phi denotes the Euler function.

On realizability of p-groups as Galois groups

2000 Mathematics Subject Classification: 12F12, 15A66.

On automorphisms of split metacyclic groups

Let D( m, n; k) be the semi-direct product of two finite cyclic groups Z/m = < x > and Z/n = < y >, where the action is given by yxy(-1) = x(k). In particular, this includes the dihedral groups D(2m). We calculate the automorphism group Aut (D(m, n; k)).

On invariant Rings of Sylow subgroups of finite classical groups

In this thesis we study the invariant rings for the Sylow p-subgroups of the nite classical groups. We have successfully constructed presentations for the invariant rings for the Sylow p-subgroups of the unitary groups GU(3; Fq2) and GU(4; Fq2 ), the symplectic group Sp(4; Fq) and the orthogonal group O+(4; Fq) with q odd. In all cases, we obtained a minimal generating set which is also a SAGBI basis. Moreover, we computed the relations among the generators and showed that the invariant ring for these groups are a complete intersection. This shows that, even though the invariant rings of the Sylow p-subgroups of the general linear group are polynomial, the same is not true for Sylow p-subgroups of general classical groups. We also constructed the generators for the invariant elds for the Sylow p-subgroups of GU(n; Fq2 ), Sp(2n; Fq), O+(2n; Fq), O-(2n + 2; Fq) and O(2n + 1; Fq), for every n and q. This is an important step in order to obtain the generators and relations for the invariant rings of all these groups.

Generalized soluble groups of finite co-central rank

Eine Gruppe G hat endlichen Prüferrang (bzw. Ko-zentralrang) kleiner gleich r, wenn für jede endlich erzeugte Gruppe H gilt: H (bzw. H modulo seinem Zentrum) ist r-erzeugbar. In der vorliegenden Arbeit werden, soweit möglich, die bekannten Sätze über Gruppen von endlichem Prüferrang (kurz X-Gruppen), auf die wesentlich größere Klasse der Gruppen mit endlichem Ko-zentralrang (kurz R-Gruppen) verallgemeinert.Für lokal nilpotente R-Gruppen, welche torsionsfrei oder p-Gruppen sind, wird gezeigt, dass die Zentrumsfaktorgruppe eine X-Gruppe sein muss. Es folgt, dass Hyperzentralität und lokale Nilpotenz für R-Gruppen identische Bediungungen sind. Analog hierzu sind R-Gruppen genau dann lokal auflösbar, wenn sie hyperabelsch sind. Zentral für die Strukturtheorie hyperabelscher R-Gruppen ist die Tatsache, dass solche Gruppen eine aufsteigende Normalreihe abelscher X-Gruppen besitzen. Es wird eine Sylowtheorie für periodische hyperabelsche R-Gruppen entwickelt. Für torsionsfreie hyperabelsche R-Gruppen wird deren Auflösbarkeit bewiesen. Des weiteren sind lokal endliche R-Gruppen fast hyperabelsch. Für R-Gruppen fallen sehr große Gruppenklassen mit den fast hyperabelschen Gruppen zusammen. Hierzu wird der Begriff der Sektionsüberdeckung eingeführt und gezeigt, dass R-Gruppen mit fast hyperabelscher Sektionsüberdeckung fast hyperabelsch sind.

Groups Acting on Tensor Products

Groups preserving a distributive product are encountered often in algebra. Examples include automorphism groups of associative and nonassociative rings, classical groups, and automorphism groups of p-groups. While the great variety of such products precludes any realistic hope of describing the general structure of the groups that preserve them, it is reasonable to expect that insight may be gained from an examination of the universal distributive products: tensor products. We give a detailed description of the groups preserving tensor products over semisimple and semiprimary rings, and present effective algorithms to construct generators for these groups. We also discuss applications of our methods to algorithmic problems for which all currently known methods require an exponential amount of work. (C) 2013 Elsevier B.V. All rights reserved.

Enhanced electro-oxidation resistance of carbon electrodes induced by phosphorus surface groups

The electro-oxidation of carbon materials enormously degrades their performance and limits their wider utilization in multiple electrochemical applications. In this work, the positive influence of phosphorus functionalities on the overall electrochemical stability of carbon materials has been demonstrated under different conditions. We show that the extent and selectivity of electroxidation in P-containing carbons are completely different to those observed in conventional carbons without P. The electro-oxidation of P-containing carbons involves the active participation of phosphorus surface groups, which are gradually transformed at high potentials from less-to more-oxidized species to slow down the introduction of oxygen groups on the carbon surface (oxidation) and the subsequent generation of (C*OOH)-like unstable promoters of electro-gasification. The highest-oxidized P groups (–C–O–P-like species) seem to distribute the gained oxygen to neighboring carbon sites, which finally suffer oxidation and/or gasification. So it is thought that P-groups could act as mediators of carbon oxidation although including various steps and intermediates compared to electroxidation in P-free materials.

Isomorphism of Commutative Group Algebras of Finite Abelian Groups

Let a commutative ring R be a direct product of indecomposable rings with identity and let G be a finite abelian p-group. In the present paper we give a complete system of invariants of the group algebra RG of G over R when p is an invertible element in R. These investigations extend some classical results of Berman (1953 and 1958), Sehgal (1970) and Karpilovsky (1984) as well as a result of Mollov (1986).

Structure, bonding state and in-vitro study of Ca–P–Ti film deposited on Ti6Al4V by RF magnetron sputtering

Experimental investigation of functionally graded calcium phosphate-based bio-active films on Ti-6A1-4V orthopaedic alloy prepared in an RF magnetron sputtering plasma reactor is reported. The technique involves concurrent sputtering of Hydroxyapatite (HA) and Ti targets, which results in remarkably enhanced adhesion of the film to the substrate and stability of the interface. The films have been characterized using X-ray diffraction (XRD) and X-ray photoelectron spectroscopy (XPS). The XPS data show that the films are composed of O, Ca, P and Ti, and reveal the formation of O=P groups and hybridization of O-Ca-P. The XRD pattern shows that the Ca-P thin films are of crystalline calcium oxide phosphate (4CaO·P2O5) with preferred orientation varying with processing parameters. High-resolution optical emission spectra show that the emission of CaO is dominant. The CaO, PO and CaPO species are strongly influenced by deposition conditions. The introduction of Ti element during deposition provides a stable interface between bio-inert substrates Ti-6A1-4V and bioactive HA coating. In-vitro cell culturing tests suggest excellent biocompatibility of the Ca-P-Ti films.

On an embedding property of generalized Carter subgroups

If E and F are saturated formations, we say that E is strongly contained in F if for any solvable group G with E-subgroup, E, and F-subgroup, F, some conjugate of E is contained in F. In this paper, we investigate the problem of finding the formations which strongly contain a fixed saturated formation E.

Our main results are restricted to formations, E, such that E = {G|G/F(G) ϵT}, where T is a non-empty formation of solvable groups, and F(G) is the Fitting subgroup of G. If T consists only of the identity, then E=N, the class of nilpotent groups, and for any solvable group, G, the N-subgroups of G are the Carter subgroups of G.

We give a characterization of strong containment which depends only on the formations E, and F. From this characterization, we prove:

If T is a non-empty formation of solvable groups, E = {G|G/F(G) ϵT}, and E is strongly contained in F, then

(1) there is a formation V such that F = {G|G/F(G) ϵV}.

(2) If for each prime p, we assume that T does not contain the class, S_p’, of all solvable p’-groups, then either E = F, or F contains all solvable groups.

This solves the problem for the Carter subgroups.

We prove the following result to show that the hypothesis of (2) is not redundant:

If R = {G|G/F(G) ϵS_r’}, then there are infinitely many formations which strongly contain R.

Estudos dos efeitos antioxidantes e anti-inflamatórios da própolis sobre as células RAW 264.7 e na resposta inflamatória pulmonar aguda causada pela exposição à fumaça de cigarro em camundongos

A doença pulmonar obstrutiva crônica (DPOC) causa a redução da capacidade respiratória e seu desenvolvimento é associado à fumaça de cigarro. O cigarro possui mais de 4800 substâncias tóxicas e causa a morte de seis milhões de pessoas por ano no mundo. Estudos buscam meios de reverter os males causados pela fumaça de cigarro. A própolis (P) é um produto produzido por abelhas que possui várias propriedades. O objetivo deste trabalho foi avaliar os efeitos antioxidantes da P em macrófagos murinos e na inflamação pulmonar aguda induzida pela fumaça de cigarro (CS) em camundongos. A análise dos compostos fitoquímicos do extrato alcóolico da P (EAP) foi feita por cromatografia gasosa acoplada à espectrometria de massa (GC-MS). Células da linhagem RAW 264.7 foram tratadas em diversas concentrações de P durante 24 horas. Após tratamento, as seguintes análises foram realizadas: polifenóis totais; viabilidade celular (MTT); potencial redutor (DPPH); espécies reativas de oxigênio totais (ROS) e de malondialdeído (MDA). Trinta camundongos C57BL/6 foram divididos em 3 grupos (n=10/grupo): Controle+P, CS e CS+P. Ambos os grupos CS foram expostos a 6 cigarros/dia durante 5 dias. O grupo CS foi tratado com veículo. O pulmão e o lavado broncoalveolar (BAL) foram coletados para análise histológica e contagem diferencial de células. As análises para mieloperoxidase (MPO), superóxido dismutase (SOD), catalase (CAT), glutationa peroxidase (GPx), glutationa reduzida (GSH) e oxidada (GSSG), MDA, nitrito e western blotting para TNF-alfa foram realizadas. A análise fitoquímica do EAP mostrou a presença dos ácidos hidrocinâmicos e coumárico, a artepilina C e a drupanina. Foi observado o aumento concentração-dependente dos níveis de polifenóis totais (p<0,001), do MTT (p<0,001) e do DPPH (p<0,001), e o inverso com o MDA (p<0,001). Os níveis de ROS diminuem nas concentrações de 15,6 e 31,2 mg/mL (p<0,05, ambos). A histologia pulmonar do grupo Controle+P foi similar ao do CS+P e foi observado um influxo de macrófagos e neutrófilos no grupo CS (p<0,01 e p<0,001, respectivamente). Os níveis de MPO foram aumentados no grupo CS (526,534,72 mU/mg ptn, p<0,01), mas houve uma redução no grupo CS+P (385,127,64 mU/mg ptn, p<0,05) comparável ao Controle+P (13412,99 mU/mg ptn, p<0,001), o mesmo aconteceu com as enzimas antioxidantes: SOD (Controle+P: 523,529,6 U/mg ptn; CS: 523,529,6 U/mg ptn, p<0,001; CS+P: 246,815,69 U/mg ptn, p<0,001); CAT (Controle+P: 37,383,39 U/mg ptn; CS: 92,686,24 U/mg ptn, p<0,001; CS+P: 59,844,55 U/mg ptn, p<0,05); GPx (Controle+P: 2,230,17 (M/min/mg ptn) x 10-1; CS: 4,510,31 (M/min/mg ptn) x 10-1, p<0,001; CS+P: 2,640,19 (M/min/mg ptn) x 10-1, p<0,05). O inverso ocorreu com a relação GSH/GSSG (Controle+P: 1,0880,17; CS: 0,7360,07, p<0,05; CS+P: 1,2580,10, p<0,05). Os níveis de MDA (Controle+P: 0,2660,05 nMol/mg ptn; CS: 0,940,076 nMol/mg ptn, p<0,001; CS+P: 0,4980,06 nMol/mg ptn, p<0,01) e de nitrito (Controle+P: 50,014,19 Mol/mg ptn; CS: 108,77,73 Mol/mg ptn, p<0,001; CS+P: 58,843,42 nMol/mg ptn, p<0,01) estavam aumentados no CS que em outros grupos. A expressão de TNF-α foi observada no grupo CS. O tratamento da P apresentou ação anti-inflamatória e antioxidante em macrófagos e em camundongos expostos à fumaça de cigarro, possivelmente pela ação dos polifenóis presentes nela

Heptairon bis(phosphate) tetrakis(hydrogenphosphate)

A new iron hydrogen phosphate, heptairon bis(phosphate) tetrakis(hydrogenphosphate), Fe-7(PO4)(2)(HPO4)(4), has been prepared hydrothermally and characterized by single-crystal X-ray diffraction. The compound has one Fe atom on an inversion centre and is isostructural with Mn-7(PO4)(2)(HPO4)(4) and Co-7(PO4)(2)(HPO4)(4). The structure is based on a framework of edge- and corner-sharing FeO6, Fe-5 and PO4 polyhedra, isotypic with that found in the mixed-valence iron phosphate Fe-7(PO4)(6). The Fe atoms in the title compound are purely in the divalent state, just like the Co atoms in Co-7(PO4)(2)(HPO4)(4), the necessary charge balance being maintained by the addition of H atoms in the form of bridging Fe-OH-P groups.

A NMR-STUDY OF THE INTERACTION OF SILICA WITH DIPALMITOYLPHOSPHATIDYLCHOLINE LIPOSOMES

The interaction of silica with dipalmitoylphosphatidylcholine (DPPC) liposomes has been studied by detecting H-1 and 2D NOESY NMR spectra and measuring proton spin-lattice relaxation time (T-1). The antagonistic effect of aluminium citrate on silica has also been studied by measuring the proton T-1 values, The results show that silica particles mainly bind to the phosphate moiety of the polar headgroup of DPPC bilayers through hydrogen bonds between Si-OH and O-P groups, but they have no significant effect on the conformation of the choline group of the polar headgroup, The addition of silica particles decreases the mobilities of the hydrocarbon chains slightly, Proton T-1 data also indicate that aluminium citrate reduces the effect of silica, A possible mechanism for the toxicity of silica and the antagonistic effect of aluminium titrate on silica is suggested. (C) 1995 Academic Press Inc.