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.

Free groups in central simple algebras without Tits` theorem

Let R be a noncommutative central simple algebra, the center k of which is not absolutely algebraic, and consider units a,b of R such that {a,a(b)} freely generate a free group. It is shown that such b can be chosen from suitable Zariski dense open subsets of R, while the a can be chosen from a set of cardinality \k\ (which need not be open).

ROOT PROBLEM FOR CONVENIENT MAPS

In this paper we study when the minimal number of roots of the so-called convenient maps horn two-dimensional CW complexes into closed surfaces is zero We present several necessary and sufficient conditions for such a map to be root free Among these conditions we have the existence of specific fittings for the homomorphism induced by the map on the fundamental groups, existence of the so-called mutation of a specific homomorphism also induced by the map, and existence of particular solutions of specific systems of equations on free groups over specific subgroups

Twisted conjugacy classes in nilpotent groups

A group is said to have the R(infinity) property if every automorphism has an infinite number of twisted conjugacy classes. We study the question whether G has the R(infinity) property when G is a finitely generated torsion-free nilpotent group. As a consequence, we show that for every positive integer n >= 5, there is a compact nilmanifold of dimension n on which every homeomorphism is isotopic to a fixed point free homeomorphism. As a by-product, we give a purely group theoretic proof that the free group on two generators has the R(infinity) property. The R(infinity) property for virtually abelian and for C-nilpotent groups are also discussed.

THE LOWER CENTRAL AND DERIVED SERIES OF THE BRAID GROUPS OF THE FINITELY-PUNCTURED SPHERE

Motivated in part by the study of Fadell-Neuwirth short exact sequences, we determine the lower central and derived series for the braid groups of the finitely-punctured sphere. For n >= 1, the class of m-string braid groups B(m)(S(2)\{x(1), ... , x(n)}) of the n-punctured sphere includes the usual Artin braid groups B(m) (for n = 1), those of the annulus, which are Artin groups of type B (for n = 2), and affine Artin groups of type (C) over tilde (for n = 3). We first consider the case n = 1. Motivated by the study of almost periodic solutions of algebraic equations with almost periodic coefficients, Gorin and Lin calculated the commutator subgroup of the Artin braid groups. We extend their results, and show that the lower central series (respectively, derived series) of B(m) is completely determined for all m is an element of N (respectively, for all m not equal 4). In the exceptional case m = 4, we obtain some higher elements of the derived series and its quotients. When n >= 2, we prove that the lower central series (respectively, derived series) of B(m)(S(2)\{x(1), ... , x(n)}) is constant from the commutator subgroup onwards for all m >= 3 (respectively, m >= 5). The case m = 1 is that of the free group of rank n - 1. The case n = 2 is of particular interest notably when m = 2 also. In this case, the commutator subgroup is a free group of infinite rank. We then go on to show that B(2)(S(2)\{x(1), x(2)}) admits various interpretations, as the Baumslag-Solitar group BS(2, 2), or as a one-relator group with non-trivial centre for example. We conclude from this latter fact that B(2)(S(2)\{x(1), x(2)}) is residually nilpotent, and that from the commutator subgroup onwards, its lower central series coincides with that of the free product Z(2) * Z. Further, its lower central series quotients Gamma(i)/Gamma(i+1) are direct sums of copies of Z(2), the number of summands being determined explicitly. In the case m >= 3 and n = 2, we obtain a presentation of the derived subgroup, from which we deduce its Abelianization. Finally, in the case n = 3, we obtain partial results for the derived series, and we prove that the lower central series quotients Gamma(i)/Gamma(i+1) are 2-elementary finitely-generated groups.

The lower central and derived series of the braid groups of the projective plane

In this paper, we determine the lower central and derived series for the braid groups of the projective plane. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is interesting in its own right. The n-string braid groups B(n)(RP(2)) of the projective plane RP(2) were originally studied by Van Buskirk during the 1960s. and are of particular interest due to the fact that they have torsion. The group B(1)(RP(2)) (resp. B(2)(RP(2))) is isomorphic to the cyclic group Z(2) of order 2 (resp. the generalised quaternion group of order 16) and hence their lower central and derived series are known. If n > 2, we first prove that the lower central series of B(n)(RP(2)) is constant from the commutator subgroup onwards. We observe that Gamma(2)(B(3)(RP(2))) is isomorphic to (F(3) X Q(8)) X Z(3), where F(k) denotes the free group of rank k, and Q(8) denotes the quaternion group of order 8, and that Gamma(2)(B(4)(RP(2))) is an extension of an index 2 subgroup K of P(4)(RP(2)) by Z(2) circle plus Z(2). As for the derived series of B(n)(RP(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group B(n)(RP(2)) being finite and soluble for n <= 2, the critical cases are n = 3, 4. We are able to determine completely the derived series of B(3)(RP(2)). The subgroups (B(3)(RP(2)))((1)), (B(3)(RP(2)))((2)) and (B(3)(RP(2)))((3)) are isomorphic respectively to (F(3) x Q(8)) x Z(3), F(3) X Q(8) and F(9) X Z(2), and we compute the derived series quotients of these groups. From (B(3)(RP(2)))((4)) onwards, the derived series of B(3)(RP(2)), as well as its successive derived series quotients, coincide with those of F(9). We analyse the derived series of B(4)(RP(2)) and its quotients up to (B(4)(RP(2)))((4)), and we show that (B(4)(RP(2)))((4)) is a semi-direct product of F(129) by F(17). Finally, we give a presentation of Gamma(2)(B(n)(RP(2))). (C) 2011 Elsevier Inc. All rights reserved.

Determination of polyamines in organic extracts from roots of Canavalia ensiformis by capillary electrophoresis

A rapid, selective and specific capillary zone electrophoresis method to determine polyamines in organic extracts from roots of Canavalia ensiformis (Jack Beans) was developed using ultra violet (UV) detection. Canavalia ensiformis is relatively free from diseases and it is used as reference in allelopathy studies. Polyamines are widely distributed in plant and it could be involved in plant pathogen interactions. Optimal separation was achieved using 15 mmol.L-1formic acid (pH 3.0) + 4 mmol.L-1 imidazole as a background electrolyte. It was possible to identify and quantify the polyamines on herbal samples in the presence of other phytochemical substances and analyze them quickly (up to 6 min). The applicability of this method was evaluated in crude organic extracts from roots of Canavalia ensiformis.

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.

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.

A group topology on the free abelian group of cardinality c that makes its square countably compact

Under p = c, we prove that it is possible to endow the free abelian group of cardinality c with a group topology that makes its square countably compact. This answers a question posed by Madariaga-Garcia and Tomita and by Tkachenko. We also prove that there exists a Wallace semigroup (i.e., a countably compact both-sided cancellative topological semigroup which is not a topological group) whose square is countably compact. This answers a question posed by Grant.

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.

Effects of Early Functional Loading on Maintenance of Free Autogenous Bone Graft and Implant Osseointegration: An Experimental Study in Dogs

Purpose: The aim of the present study was to investigate the healing, integration, and maintenance of autogenous onlay bone grafts and implant osseointegration either loaded in the early or the delayed stages. Materials and Methods: A total of 5 male clogs received bilateral blocks of onlay bone grafts harvested from the contralateral alveolar ridge of the mandible. On one side, the bone block was secured by 3 dental implants (3.5 mm x 13.0 mm, Osseospeed; Astra Tech AB, Molndal, Sweden). Two implants at the extremities of the graft were loaded 2 clays after installation by abutment connection and prosthesis (simultaneous implant placement group); the implant in the middle remained unloaded and served as the control. On the other side, the block was fixed with 2 fixation screws inserted in the extremities of the graft. Four weeks later, the fixation screws were replaced with 3 dental implants. The loading procedure (delayed implant placement group) was performed 2 clays later, as described for the simultaneous implant placement sites. The animals were sacrificed 12 weeks after the grafting procedure. Implant stability was measured through resonance frequency analysis. The bone volume and density were assessed on computed tomography. The bone to implant contact and bone area in a region of interest were evaluated on histologic slides. Results: The implant stability quotient showed statistical significance in favor of the delayed loaded grafts (P=.001). The bone-to-implant contact (P=.008) and bone area in a region of interest (P=0.005) were significantly greater in the delayed group. Nevertheless, no difference was found in terms of graft volume and density between the early loaded and delayed-loaded approaches. Conclusions: The protocol in which the implant and bone graft were given delayed loading allows for effective quality of implant osseointegration and stabilization, with healing and remodeling occurring in areas near the implant resulting in denser bone architecture. (C) 2010 American Association of Oral and Maxillofacial Surgeons J Oral Maxillofac Sing 68:825-832, 2010

Effects of supplementation with free glutamine and the dipeptide alanyl-glutamine on parameters of muscle damage and inflammation in rats submitted to prolonged exercise

In this study, we investigated the effect of the supplementation with the dipeptide L-alanyl-L-glutamine (DIP) and a solution containing L-glutamine and L-alanine on plasma levels markers of muscle damage and levels of pro-inflammatory cytokines and glutamine metabolism in rats submitted to prolonged exercise. Rats were submitted to sessions of swim training for 6 weeks. Twenty-one days prior to euthanasia, the animals were supplemented with DIP (n = 8) (1.5 g.kg(-1)), a solution of free L-glutamine (1 g.kg(-1)) and free L-alanine (0.61 g.kg(-1)) (G&A, n = 8) or water (control (CON), n = 8). Animals were killed at rest before (R), after prolonged exercise (PE-2 h of exercise). Plasma concentrations of glutamine, glutamate, tumour necrosis factor-alpha (TNF-alpha), prostaglandin E2 (PGE2) and activity of creatine kinase (CK), lactate dehydrogenase (LDH) and muscle concentrations Of glutamine and glutamate were measured. The concentrations of plasma TNF-alpha, PGE2 and the activity of CK were lower in the G&A-R and DIP-R groups, compared to the CON-R. Glutamine in plasma (p < 0.04) and soleus muscle (p < 0.001) was higher in the DIP-R and G&A-R groups relative to the CON-R group. G&A-PE and DIP-PE groups exhibited lower concentrations of plasma PGE2 (p < 0.05) and TNF-alpha (p < 0.05), and higher concert I rations of glutamine and glutamate in soleus (p < 0.001) and gastrocnemius muscles (p < 0.05) relative to the CON-PE group. We concluded that supplementation with free L-glutamine and the dipeptide LL-alanyl-LL-glutamine represents an effective source of glutamine, which may attenuate inflammation biomarkers after periods of training and plasma levels of CK and the inflammatory response induced by prolonged exercise. Copyright (C) 2009 John Wiley & Sons, Ltd.

Proton flux induced by free fatty acids across phospholipid bilayers: New evidences based on short-circuit measurements in planar lipid membranes

Free fatty acids (FFA) are important mediators of proton transport across membranes. However, information concerning the influence of the Structural features of both FFA and the membrane environment on the proton translocation mechanisms across phospholipid membranes is relatively scant. The effects of FFA chain length, unsaturation and membrane composition on proton transport have been addressed in this study by means of electrical measurements in planar lipid bilayers. Proton conductance (G(H)(+)) was calculated from open-circuit voltage and short-circuit current density measurements. We found that cis-unsaturated FFA caused a more pronounced effect on proton transport as compared to Saturated and trans-unsaturated FFA. Cholesterol and cardiolipin decreased membrane leak conductance. Cardiolipin also decreased proton conductance. These effects indicate a dual modulation of protein-independent proton transport by FFA: through a flip-flop mechanism and by modifying a proton diffusional pathway. Moreover the membrane phospholipid composition was shown to importantly affect both processes. (C) 2009 Elsevier Inc. All rights reserved.

BnP1, a novel P-I metalloproteinase from Bothrops neuwiedi venom: Biological effects benchmarking relatively to jararhagin, a P-IIISVMP

Snake venom metalloproteinases (SVMPs) have been extensively studied and their effects associated with the local bleeding observed in human accidents by viper snakes. Representatives of P-I and P-III classes of SVMPs similarly hydrolyze extracellular matrix proteins or coagulation factors while only P-III SVMPs induce significant hemorrhage in experimental models. In this work, the effects of P-I and P-III SVMPs on plasma proteins and cultures of muscle and endothelial cells were compared in order to enlighten the mechanisms involved in venom-induced hemorrhage. To reach this comparison, BnP1 was isolated from B. neuwiedi venom and used as a weakly hemorrhagic P-I SVMPs and jararhagin was used as a model of potently hemorrhagic P-III SVMP. BnP1 was isolated by size exclusion and anion-exchange chromatographies, showing apparent molecular mass of approximately 24kDa and sequence similarity with other members of SVMPs, which allowed its classification as a group P-I SVMP. The comparison of local effects induced by SVMPs showed that BnP1 was devoid of significant myotoxic and hemorrhagic activities and jararhagin presented only hemorrhagic activity. BnP1 and jararhagin were able to hydrolyze fibrinogen and fibrin, although the latter displayed higher activity in both systems. Using HUVEC primary cultures, we observed that BnP1 induced cell detachment and a decrease in the number of viable endothelial cells in levels comparable to those observed by treatment with jararhagin. Moreover, both BnP1 and jararhagin induced apoptosis in HUVECs while only a small increase in LDH supernatant levels was observed after treatment with jararhagin, suggesting that the major mechanism involved in endothelial cell death is apoptosis. Jararhagin and BnP1 induced little effects on C2C12 muscle cell cultures, characterized by a partial detachment 24h after treatment and a mild necrotic effect as evidenced by a small increase in the supernatants LDH levels. Taken together, our data show that P-I and P-III SVMPs presented comparable effects except for the hemorrhagic activity, suggesting that hydrolysis of coagulation factors or damage to endothelial cells are not sufficient for induction of local bleeding. (C) 2007 Elsevier Ltd. All rights reserved.