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.

On the manifold structure of the set of unparameterized embeddings with low regularity

Given manifolds M and N, with M compact, we study the geometrical structure of the space of embeddings of M into N, having less regularity than C(infinity) quotiented by the group of diffeomorphisms of M.

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.

Prevalence of hepatitis B and C serological markers among first-time blood donors in Brazil: A multi-center serosurvey

Little data are available on the seroprevalence of, and risk factors for hepatitis B and C viruses (HBV and HCV) infection in Latin American countries. A multi-center serosurvey was conducted among 3,598 first-time blood donors (65% men) from Sao Paulo, Salvador and Manaus in Brazil. The gender-specific seroprevalences of antibodies against hepatitis B core antigen (anti-HBc) and of the hepatitis B surface antigen (HBsAg) in anti-HBc-positive sera were measured, and risk factors analyzed by gender. The gender-specific seroprevalences of antibodies against HCV (anti-HCV) were measured, but risk factors for HCV were not determined. Anti-HBc and HBsAg seroprevalences were not significantly different in men [101/2,341 (4.31%) and 4/2,229 (0.18%), respectively] and women [65/1,237 (5.25%) and 8/ 1,169 (0.68%), respectively], whereas the seroprevalence of anti-HCV was higher in women (12/1,238 [0.97%] vs. 9/2,353 [0.38%]; odds ratio [OR] = 2.49; 95% confidence interval [Cl]: 1.0-6.0). No significant difference for HBV infection was found across the three study sites or by ethnic group. The seroprevalence of anti-HBc increased with age, but decreased with education level in both genders. Lifetime number of sexual partners was associated with anti-HBc prevalence among men (OR = 1.95; 95% Cl: 1.2-3.1), but not women. The seroprevalence of HBV and HCV was low among Brazilian blood donors, and exposure increased with age in both genders.