Nonsoluble and non-p-soluble length of finite groups

Every finite group G has a normal series each of whose factors either is soluble or is a direct product of nonabelian simple groups. We define the nonsoluble length λ(G) as the number of nonsoluble factors in a shortest series of this kind. Upper bounds for λ(G) appear in the study of various problems on finite, residually finite, and profinite groups. We prove that λ(G) is bounded in terms of the maximum 2-length of soluble subgroups of G, and that λ(G) is bounded by the maximum Fitting height of soluble subgroups. For an odd prime p, the non-p-soluble length λ p (G) is introduced, and it is proved that λ p (G) does not exceed the maximum p-length of p-soluble subgroups. We conjecture that for a given prime p and a given proper group variety V the non-p-soluble length λ p (G) of finite groups G whose Sylow p-subgroups belong to V is bounded. In this paper we prove this conjecture for any variety that is a product of several soluble varieties and varieties of finite exponent. As an application of the results obtained, an error is corrected in the proof of the main result of the second author’s paper Multilinear commutators in residually finite groups, Israel Journal of Mathematics 189 (2012), 207–224

Improvement of the Epidemiological Surveillance over Brucellosis Using GIS-Technologies

Put forward is the method of usage of Arc GIS 10 software product for epidemiological surveillance over brucellosis in the Stavropol region (SR). Designed is the structure of databases on epidemiology and epizootiology of brucellosis in the constituent entity of the Russian Federation. Constructed are two databases (Epidemiology of brucellosis in the SR and Epizootiology of brucellosis in the SR) compatible with Arc GIS 10. Carried out is the zoning of the SR territories based on assessment of the risk of infecting with brucellosis, using Arc GIS computer program

Epidemiological Welfare Provision in the Republic of Dagestan in View of Travel Industry Boost

Sustainable growth of touristic economy sector in the Republic of Dagestan exposes the need for well-timed and adequate response to epidemic and ecological hazards. In this connection investigated have been several peculiarities specific to economic activity and medical services of the republic, which precondition a threat to epidemiological welfare of the population and make possible dissemination of infections over the boundaries of republic’s natural foci

Anthrax in the Territory of Dagestan

The aim of the study is to investigate anthrax epizootiologic and epidemiologic situation in the Republic of Dagestan over the period of 1944–2010. Anthrax morbidity has been registered in 38 regions and Makhachkala. All in all 1001 anthrax cases and 3128 sick rural animals have been registered. Determined are 420 anthrax specified potentially hazardous areas (SPHA), the majority of them (77.4 %) have formed before 1969. Regions of the republic have been checked against the level of risk connected with anthrax infecting over the last 40 years. Therewith, they have been classified into three groups: with low, medium, and high epizootiological-and-epidemiological potential. 15 regions with high epizootiological-and-epidemiological potential have been marked as potentially hazardous on a regular basis. These regions occupy 31 % of the republic`s territory and 52.5 % of the SPHA territory. 84 % of patients and 88 % of fallen animals have been registered there for the past 40 years