By Jean-Camille Birget,Stuart Margolis,John Meakin,Mark V. Sapir
This quantity includes papers that are established totally on talks given at an inter nationwide convention on Algorithmic difficulties in teams and Semigroups held on the collage of Nebraska-Lincoln from could ll-May sixteen, 1998. The convention coincided with the Centennial party of the dept of arithmetic and records on the college of Nebraska-Lincoln at the get together of the single hun dredth anniversary of the granting of the 1st Ph.D. by means of the dept. investment used to be supplied by way of the USA nationwide technological know-how starting place, the dep. of Math ematics and information, and the varsity of Arts and Sciences on the college of Nebraska-Lincoln, during the College's concentration application in Discrete, Experimental and utilized arithmetic. the aim of the convention used to be to assemble researchers with pursuits in algorithmic difficulties in team thought, semigroup concept and desktop technology. a very helpful characteristic of this convention used to be that it supplied a framework for alternate of principles among the examine groups in semigroup thought and crew thought, and a number of other of the papers accumulated the following replicate this interac tion of principles. The papers gathered during this quantity characterize a go component to a few of the effects and ideas that have been mentioned within the convention. They replicate a synthesis of overlapping principles and strategies influenced via difficulties bearing on finite monoids, finitely offered mono ids, finitely provided teams and loose groups.
The booklet is meant for graduate scholars of theoretical physics (with a historical past in quantum mechanics) in addition to researchers attracted to purposes of Lie workforce conception and Lie algebras in physics. The emphasis is at the inter-relations of illustration theories of Lie teams and the corresponding Lie algebras.
The speculation of finite fields is a department of algebra that has come to the fore as a result of its different functions in such components as combinatorics, coding conception and the mathematical examine of switching ciruits. This booklet is dedicated completely to the idea of finite fields, and it presents entire insurance of the literature.
The learn of solid teams connects version idea, algebraic geometry and staff conception. It analyses teams which own a definite very basic dependence relation (Shelah's idea of 'forking'), and attempts to derive structural homes from this. those could be group-theoretic (nilpotency or solubility of a given group), algebro-geometric (identification of a gaggle as an algebraic group), or model-theoretic (description of the definable sets).
This book's target is to make obtainable strategies for learning Whitehead teams of finite teams, in addition to various comparable themes equivalent to induction idea and p-adic logarithms. the writer has integrated a long creation to set the scene for non-specialists who wish an outline of the sector, its background and its purposes.
Additional info for Algorithmic Problems in Groups and Semigroups (Trends in Mathematics)