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.

Integrated Geophysical Investigation of the St. James Fault Complex: A Case Study

We noninvasively detected the characteristics and location of a regional fault in an area of poor bedrock exposure complicated by karst weathering features in the subsurface. Because this regional fault is associated with sinkhole formation, its location is important for hazard avoidance. The bedrock lithologies on either side of the fault trace are similar; hence, we chose an approach that capitalized on the complementary strengths of very low frequency (VLF) electromagnetic, resistivity, and gravity methods. VLF proved most useful as a first-order reconnaissance tool, allowing us to define a narrow target area for further geophysical exploration. Fault-related epikarst was delineated using resistivity. Ultimately, a high-resolution gravity survey and subsequent inverse modeling using the results of the resistivity survey helped to further constrain the location and approximate orientation of the fault. The combined results indicated that the location of the fault trace needed to be adjusted 53 m south of the current published location and was consistent with a north-dipping thrust fault. Additionally, a gravity low south of the fault trace agreed with the location of conductive material from the resistivity and VLF surveys. We interpreted these anomalies to represent enhanced epikarst in the fault footwall. We clearly found that a staged approach involving a progression of methods beginning with a reconnaissance VLF survey, followed by high-resolution gravity and electrical resistivity surveys, can be used to characterize a fault and fault-related karst in an area of poor bedrock surface exposure.