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.

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.

On Groups with Two Isomorphism Classes of Derived Subgroups

The structure of groups which have at most two isomorphism classes of derived subgroups (D-2-groups) is investigated. A complete description of D-2-groups is obtained in the case where the derived subgroup is finite: the solution leads an interesting number theoretic problem. In addition, detailed information is obtained about soluble D-2-groups, especially those with finite rank, where algebraic number fields play an important role. Also, detailed structural information about insoluble D-2-groups is found, and the locally free D-2-groups are characterized.

Agricultural Policymaking: Interest Groups and Access to Governmental Officials

Conservation agriculture that focuses on soil recovery is both economically and environmentally sustainable. This lies in contrast with many of the current agricultural practices, which push for high production, which, in turn lead to over-depletion of the soil. Agricultural interest groups play a role in crafting farming policies with governmental officials. Therefore, my study examined three interest group types agribusinesses, farmer organizations, and environmental NGOs that seek to influence agricultural policy, specifically focusing on the federal farm bill, due to its large impact throughout the nation. The research in which data wasgathered through subject interviews, a literature review, and databases found that access to governmental officials affects the amount of influence a group can have. Access is contingent upon: 1) the number of networks (social, professional, and political), 2) amount of money spent through campaign contributions and lobbying expenditures, and 3) extent of business enterprises and subsidiaries. The evidence shows that there is a correlation between these variables and the extent of access. My research concludes that agribusiness interest groups have the most access to government officials, and thus have the greatest influence on agricultural policies. Because agribusinesses support subsidies of commodity-crops this indirectly impacts conservation agriculture, as the two programs compete in a zero-sum game for funding in the farm bills.