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The aim of this volume is to provide a compendium of state of the art overview chapters by leading research, from diverse scientific fields, who share a common involvement in understanding and utilizing the interactions between chemicals and plant leaves.
How many groups of order n are there? This is a natural question for anyone studying group theory, and this Tract provides an exhaustive and up-to-date account of research into this question spanning almost fifty years. The authors presuppose an undergraduate knowledge of group theory, up to and including Sylow's Theorems, a little knowledge of how a group may be presented by generators and relations, a very little representation theory from the perspective of module theory, and a very little cohomology theory - but most of the basics are expounded here and the book is more or less self-contained. Although it is principally devoted to a connected exposition of an agreeable theory, the book does also contain some material that has not hitherto been published. It is designed to be used as a graduate text but also as a handbook for established research workers in group theory.
William Burnside [1852-1927] was a scholar of international renown, a colourful figure, and a pure mathematician who established abstract algebra as a subject of serious study in Britain. This edition of Collected Papers, enhanced by a series of critical essays, is of major importance to scholars in group theory and the history of mathematics.
The book, based on a course of lectures by the authors at the Indian Institute of Technology, Guwahati, covers aspects of infinite permutation groups theory and some related model-theoretic constructions. There is basic background in both group theory and the necessary model theory, and the following topics are covered: transitivity and primitivity; symmetric groups and general linear groups; wreatch products; automorphism groups of various treelike objects; model-theoretic constructions for building structures with rich automorphism groups, the structure and classification of infinite primitive Jordan groups (surveyed); applications and open problems. With many examples and exercises, the book is intended primarily for a beginning graduate student in group theory.
"Groups and Geometry" contains the Oxford Mathematical Institute notes for undergraduates and first-year postgraduates. The content, although guided by the Oxford syllabus, covers other material, some introductory and some that, because of limited time, had to be excluded from or curtailed in the syllabus. This book is about the measurement of symmetry, which is what groups are for. Symmetry is visable in all parts of mathematics and in many other areas, and geometrical symmetry is the most visable of all. For this reason, groups and geometry are close neighbours. The first half of the book (chapters 1-9) covers groups and the second half (chapters 10-18) covers geometry, with the symbiotic relationship between the two more than justifying the union. Both parts contain a number of exercises that should be helpful to the reader wishing to gain a fuller understanding of this area of mathematics.
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