The first group (co)homology of a group G with coefficients in some G-modules

Let G be a group. We give some formulas for the first group homology and cohomology of a group G with coefficients in an arbitrary G-module (Z) over tilde. More explicit calculations are done in the special cases of free groups, abelian groups and nilpotent groups. We also perform calculations for certain G-module M, by reducing it to the case where the coefficient is a G-module (Z) over tilde. As a result of the well known equalities H-1(X, M) = H-1(pi(1)(X), M) and H-1(X, M) = H-1(pi(1) (X), M), for any G-module M, we are able to calculate the first homology and cohomology groups of topological spaces with certain local system of coefficients.

Bicyclic units, Bass cyclic units and free groups

Let G be a finite group and ZG its integral group ring. We show that if alpha is a nontrivial bicyclic unit of ZG, then there are bicyclic units beta and gamma of different types, such that and are non-abelian free groups. In the case when G is non-abelian of order coprime to 6 we prove the existence of a bicyclic unit u and a Bass cyclic unit v in ZG, such that < u(m), v > is a free non-abelian group for all sufficiently large positive integers m.

INVOLUTIONS AND FREE PAIRS OF BASS CYCLIC UNITS IN INTEGRAL GROUP RINGS

Let ZG be the integral group ring of the finite nonabelian group G over the ring of integers Z, and let * be an involution of ZG that extends one of G. If x and y are elements of G, we investigate when pairs of the form (u(k,m)(x*), u(k,m)(x*)) or (u(k,m)(x), u(k,m)(y)), formed respectively by Bass cyclic and *-symmetric Bass cyclic units, generate a free noncyclic subgroup of the unit group of ZG.

BASS CYCLIC UNITS AS FACTORS IN A FREE GROUP IN INTEGRAL GROUP RING UNITS

Marciniak and Sehgal showed that if u is a non-trivial bicyclic unit of an integral group ring then there is a bicyclic unit v such that u and v generate a non-abelian free group. A similar result does not hold for Bass cyclic units of infinite order based on non-central elements as some of them have finite order modulo the center. We prove a theorem that suggests that this is the only limitation to obtain a non-abelian free group from a given Bass cyclic unit. More precisely, we prove that if u is a Bass cyclic unit of an integral group ring ZG of a solvable and finite group G, such that u has infinite order modulo the center of U(ZG) and it is based on an element of prime order, then there is a non-abelian free group generated by a power of u and a power of a unit in ZG which is either a Bass cyclic unit or a bicyclic unit.

ALTERNATING UNITS AS FREE FACTORS IN THE GROUP OF UNITS OF INTEGRAL GROUP RINGS

Let G be a group of odd order that contains a non-central element x whose order is either a prime p >= 5 or 3(l), with l >= 2. Then, in U(ZG), the group of units of ZG, we can find an alternating unit u based on x, and another unit v, which can be either a bicyclic or an alternating unit, such that for all sufficiently large integers m we have that < u(m), v(m)> = < u(m)> * < v(m)> congruent to Z * Z.

Involutions and free pairs of bicyclic units in integral group rings

If * : G -> G is an involution on the finite group G, then * extends to an involution on the integral group ring Z[G] . In this paper, we consider whether bicyclic units u is an element of Z[G] exist with the property that the group < u, u*> generated by u and u* is free on the two generators. If this occurs, we say that (u, u*)is a free bicyclic pair. It turns out that the existence of u depends strongly upon the structure of G and on the nature of the involution. One positive result here is that if G is a nonabelian group with all Sylow subgroups abelian, then for any involution *, Z[G] contains a free bicyclic pair.

Equivariant Nielsen root theory for G-maps

Let X be a compact Hausdorff space, Y be a connected topological manifold, f : X -> Y be a map between closed manifolds and a is an element of Y. The vanishing of the Nielsen root number N(f; a) implies that f is homotopic to a root free map h, i.e., h similar to f and h(-1) (a) = empty set. In this paper, we prove an equivariant analog of this result for G-maps between G-spaces where G is a finite group. (C) 2010 Elsevier B.V. All rights reserved.

Superoxide radical protects liposome-contained cytochrome c against oxidative damage promoted by peroxynitrite and free radicals

The effects of nitrosative species on cyt c structure and peroxidase activity were investigated here in the presence of O(2)(center dot-) and anionic and zwitterionic vesicles. Nitrosative species were generated by 3-morpholinesydnonymine (SIN1) decomposition, using cyt c heme iron and/or molecular oxygen as electron acceptor. Far-and near-UV CD spectra of SIN1-treated cyt c revealed respectively a slight decrease of a-helix content (from 39 to 34%) and changes in the tryptophan structure accompanied by increased fluorescence. The Soret CD spectra displayed a significant decrease of the positive signal at 403 nm. EPR spectra revealed the presence of a low-spin cyt c form (S = 1/2) with g(1) = 2.736, g(2) = 2.465, and g(3) = 2.058 after incubation with SIN1. These data suggest that the concomitant presence of NO(center dot) and O(2)(center dot-) generated from dissolved oxygen, in a system containing cyt c and liposomes, promotes chemical and conformational modi. cations in cyt c, resulting in a hypothetical bis-histidine hexacoordinated heme iron. We also show that, paradoxically, O(2)(center dot-) prevents not only membrane lipoperoxidation by peroxide-derived radicals but also oxidation of cyt c itself due to the ability of O(2)(center dot-) to reduce heme iron. Finally, lipoperoxidation measurements showed that, although it is a more efficient peroxidase, SIN1-treated cyt c is not more effective than native cyt c in promoting damage to anionic liposomes in the presence of tert-ButylOOH, probably due to loss of affinity with negatively charged lipids. (C) 2009 Elsevier Inc. All rights reserved.

Total phenolic content and free radical scavenging activities of methanolic extract powders of tropical fruit residues

Methanolic extract powders of acerola, passion fruit and pineapple industrial residues, including pulp, seeds and peel, altogether (except for acerola) devoid of seeds, were screened for antioxidant capacity. The total phenolic contents (TPCs) of the extract powders were compared with their radical-scavenging activities (RSA) against both DPPH(center dot) and superoxide anion (O(2)(center dot-)) radicals, and their protective effect against liposome peroxidation, triggered by peroxyl radical. Lipid peroxidation was followed by the fluorescence decay of the probe, 4,4-difluoro-5-(4-phenyl-1,3-butadienyl)-4-bora-3a,4a-diaza-s-indacene-3-undecanoic acid (C(11)-BODIPY(581/591)). The TPCs of acerola, passion fruit and pineapple extract powders were (94.6 +/- 7.4); (41.2 +/- 4.2) and (9.1 +/- 1.3) mg of gallic acid equivalents g(-1) of dry extract, respectively. Acerola showed the best RSA-DPPH(center dot) scores, whereas passion fruit was more protective on the RSA-O(2)(center dot-) system. Together with the protective effects against lipid peroxidation (rate of BODIPY decay) which, were similar for acerola and passion fruit extracts, these data suggest that the methanolic extracts of acerola and passion fruit residues may be useful as antioxidant supplements, particularly the acerola extract, due to its high phenolic content. (C) 2008 Elsevier Ltd. All rights reserved

Hydrolytic Activity of Free and Immobilized Cellulase

Cellulase is an enzymatic complex which synergically promotes the degradation of cellulose to glucose. The adsorption behavior of cellulase from Trichoderma reesei onto Si wafers or amino-terminated surfaces was investigated by means of ellipsometry and atomic force microscopy (AFM) as a function of temperature. Upon increasing temperature from (24 +/- 1) to (60 +/- 1) degrees C, adsorption of cellulase became faster and more pronounced and the mean roughness of cellulase adsorbed layers increased. In the case of cellulase adsorbed onto Si wafers, Arrhenius`s plot allowed us to estimate the adsorption energy as 24.2 kJ mol(-1). The hydrolytic activity of free cellulase and cellulase immobilized onto Si wafers was tested using cellulose dispersions as substrates. The incubation temperature ranged from (37 +/- 1) to (60 +/- 1) degrees C. The highest efficiency was observed at (60 +/- 1) degrees C. The amount of glucose produced by free cellulase was similar to 20% higher than that obtained from immobilized cellulase. However, immobilizing cellulase onto Si wafers proved to be advantageous because they could be reused six times while retaining their original activity level. Such an effect was attributed to surface hydration, which prevents enzyme denaturation. The hydrolytic activity of cellulase immobilized onto amino-terminated surfaces was slightly lower than that observed for cellulase adsorbed onto Si wafers, and reuse was not possible.