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 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.

Assessing Commonality and Differentiation for Packaging-Family Planning with Application to Medication Labels

This thesis presents a metric for assessing the commonality and differentiation of packaging-family planning with application to medical labels along with supporting background research and findings. Consumable products such as medications rely on the package or label to represent the contents. Package confusion has been widely recognized as a major problem for both over-the-counter and pharmacy-dispensed medications with potentially lethal consequences. It is critical to identify a medication as a member of a product family and differentiate its contributing elements based on visual features on the package or label to avoid consumer confusion and reduce dispensing errors. Indices that indicate degrees of commonality and differentiation of features in consumer products such as batteries, light bulbs, handles, etc for platforms have been shown to benefit development of engineered product families [6]. It is possible to take a similar approach for visual features in packaging such as typography, shape/form, imagery and color to benefit packaging-family development. This thesis establishes a commonality differentiation index for prominence of visual features on over-the-counter and pharmacy-dispensed medications based on occurrence, size, and location of features. It provides a quantitative measure to assist package designers in evaluating alternatives to satisfy strategic goals and improve safety. The index is demonstrated with several medications that have been identified by the Institute for Safe Medication Practice as commonly confused.