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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 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.
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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