Locally finite groups with all subgroups either subnormal or nilpotent-by-Chernikov

Let G be a locally finite group satisfying the condition given in the title and suppose that G is not nilpotent-by-Chernikov. It is shown that G has a section S that is not nilpotent-by-Chernikov, where S is either a p-group or a semi-direct product of the additive group A of a locally finite field F by a subgroup K of the multiplicative group of F, where K acts by multiplication on A and generates F as a ring. Non-(nilpotent-by-Chernikov) extensions of this latter kind exist and are described in detail.

GROUPS THAT INVOLVE FINITELY MANY PRIMES AND HAVE ALL SUBGROUPS SUBNORMAL II

It is shown that if G is a hypercentral group with all subgroups subnormal, and if the torsion subgroup of G is a pi-group for some finite set pi of primes, then G is nilpotent. In the case where G is not hypercentral there is a section of G that is much like one of the well-known Heineken-Mohamed groups. It is also shown that if G is a residually nilpotent group with all subgroups subnormal whose torsion subgroup satisfies the above condition then G is nilpotent.

Vulnerability to risk among small farmers in Tajikistan: results of a 2011 survey

Tajikistan is judged to be highly vulnerable to risk, including food insecurity risks and climate change risks. By some vulnerability measures it is the most vulnerable among all 28 countries in the World Bank’s Europe and Central Asia Region – ECA (World Bank 2009). The rural population, with its relatively high incidence of poverty, is particularly vulnerable. The Pilot Program for Climate Resilience (PPCR) in Tajikistan (2011) provided an opportunity to conduct a farm-level survey with the objective of assessing various dimensions of rural population’s vulnerability to risk and their perception of constraints to farming operations and livelihoods. The survey should be accordingly referred to as the 2011 PPCR survey. The rural population in Tajikistan is highly agrarian, with about 50% of family income deriving from agriculture (see Figure 4.1; also LSMS 2007 – own calculations). Tajikistan’s agriculture basically consists of two groups of producers: small household plots – the successors of Soviet “private agriculture” – and dehkan (or “peasant”) farms – new family farming structures that began to be created under relevant legislation passed after 1992 (Lerman and Sedik, 2008). The household plots manage 20% of arable land and produce 65% of gross agricultural output (GAO). Dehkan farms manage 65% of arable land and produce close to 30% of GAO. The remaining 15% of arable land is held in agricultural enterprises – the rapidly shrinking sector of corporate farms that succeeded the Soviet kolkhozes and sovkhozes and today produces less than 10% of GAO (TajStat 2011) The survey conducted in May 2011 focused on dehkan farms, as budgetary constraints precluded the inclusion of household plots. A total of 142 dehkan farms were surveyed in face-to-face interviews. They were sampled from 17 districts across all four regions – Sughd, Khatlon, RRP, and GBAO. The districts were selected so as to represent different agro-climatic zones, different vulnerability zones (based on the World Bank (2011) vulnerability assessment), and different food-insecurity zones (based on WFP/IPC assessments). Within each district, 3-4 jamoats were chosen at random and 2-3 farms were selected in each jamoat from lists provided by jamoat administration so as to maximize the variability by farm characteristics. The sample design by region/district is presented in Table A, which also shows the agro-climatic zone and the food security phase for each district. The sample districts are superimposed on a map of food security phases based on IPC April 2011.

Groups Acting on Tensor Products

Groups preserving a distributive product are encountered often in algebra. Examples include automorphism groups of associative and nonassociative rings, classical groups, and automorphism groups of p-groups. While the great variety of such products precludes any realistic hope of describing the general structure of the groups that preserve them, it is reasonable to expect that insight may be gained from an examination of the universal distributive products: tensor products. We give a detailed description of the groups preserving tensor products over semisimple and semiprimary rings, and present effective algorithms to construct generators for these groups. We also discuss applications of our methods to algorithmic problems for which all currently known methods require an exponential amount of work. (C) 2013 Elsevier B.V. All rights reserved.