Let p be a prime. In this paper we investigate finite K{2,p}-groups G which have a subgroup H ? G such that K ? H = NG(K) ? Aut(K) for K a simple group of Lie type in characteristic p, and |G : H| is coprime to p. If G is of local characteristic p, then G is called almost of Lie type in characteristic p. Here G is of local characteristic p means ......
This book uses finite field theory as a hook to introduce the reader to a range of ideas from algebra and number theory. It constructs all finite fields from scratch and shows that they are unique up to isomorphism. As a payoff, several combinatorial applications of finite fields are given: Sidon sets and perfect difference sets, de Bruijn ......
INTRODUCTION 1.1 GENERAL The transport, reaction, and phase change of fluid in natural and engineered porous media rely on the knowledge gained in studying these phenomena in otherwise plain media. The presence of permeable solid (which is assumed to be rigid and stationary) influences these phenomena significantly. So fluid flow and heat ......
A characterization is given for the factorizations of almost simple groups with a solvable factor. It turns out that there are only several infinite families of these non-trivial factorizations, and an almost simple group with such a factorization cannot have socle exceptional Lie type or orthogonal of minus type. The characterization is then ......
This is an expository account of work on strong forms of the Axiom of Determinacy (AD) by a group of set theorists in Southern California, in particular by W. Hugh Woodin. The first half of the book reviews necessary background material, including the Moschovakis Coding Lemma, the existence of strong partition cardinals, and the analysis of ......
The Memoirs of the AMS is devoted to the publication of new research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers of groups of cognate papers in book form, and is under the supervision of the Editorial Committee of the AMS journal Transactions of the American Mathematical Society. All ......
Topics in Geometry, Algebra, Univariate Calculus, and Probability
Exploring Mathematics with CAS Assistance is designed as a textbook for an innovative mathematics major course in using a computer-algebra system (CAS) to investigate, explore, and apply mathematical ideas and techniques in problem solving. The book is designed modularly with student investigations and projects in number theory, geometry, algebra, ......
