Reflection principle characterizing groups in which unconditionally closed sets are algebraic

We give a necessary and sufficient condition, in terms of a certain reflection principle, for every unconditionally closed subset of a group G to be algebraic. As a corollary, we prove that this is always the case when G is a direct product of an Abelian group with a direct product (sometimes also called a direct sum) of a family of countable groups. This is the widest class of groups known to date where the answer to the 63 years old problem of Markov turns out to be positive. We also prove that whether every unconditionally closed subset of G is algebraic or not is completely determined by countable subgroups of G.Comment: 14 page

EPSTEIN - BARR VIRAL INFECTION: MODERN SITUATION AND CLINICAL-EPIDEMIOLOGICAL FEATURES AMONG FERTILE WOMEN AND NEWBORNS

Aim. The investigate the current manifestations of the symptomatic and inapparent epidemic process of Epstein-Barr infection, as well as identification of its features in women of childbearing age and newborns. Materials and methods. We performed an epidemiological analysis of the incidence of infectious mononucleosis and HIV infection in the Russian Federation. The trends of morbidity and its distribution across the territories and age groups was studied. A study was made on the frequency of detection of infection markers in women of childbearing age, incl. HIV-infected pregnant women and newborns. Results. It has been established that despite the complexity of the diagnosis, the incidence of infectious mononucleosis should be considered as an indicator of the epidemic process of the Epstein-Barr infection. Unlike healthy pregnant women, in HIV-infected pregnant women markers of acute infection that occurred without clinical manifestations were observed significantly more frequent. The maximum intensity of the active epidemic process was detected among 15 - 19 years old pregnant women who are in the latent stage of HIV with intravenous drug abuse. In older age groups of pregnant women, reinfection was observed. High incidence in newborns, as well as detection of markers of acute infection indicate the need for further research to obtain strong evidence of vertical transmission of the pathogen. Conclusion. The study showed evidence of high activity of the epidemic process of Epstein-Barr infection in fertile women. The maximum frequency of infection markers was found among HIV-infected pregnant women, which increases the risk of intrauterine infection of the fetus and newborns