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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.
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9780521882170pre July-2007 Page-i CAMBRIDGE TRACTS IN MATHEMATICS General Editors B. BOLLOBÁS, W. FULTON, A. KATOK, F. KIRWAN, P. SARNAK, B. SIMON 173 Enumeration of Finite Groups 9780521882170pre July-2007 Page-ii 9780521882170pre July-2007 Page-iii SIMON R BLACKBURN Royal Holloway, University of London PETER M NEUMANN The Queen’s College, Oxford GEETHA VENKATARAMAN St Stephen’s College, University of Delhi Enumeration of Finite Groups 9780521882170pre July-2007 Page-iv CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521882170