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OverviewThis book provides an introduction to the theory of existentially closed groups, for both graduate students and established mathematicians. It is presented from a group theoretical, rather than a model theoretical, point of view. The recursive function theory that is needed is included in the text. Interest in existentially closed groups first developed in the 1950s. This book brings together a large number of results proved since then, as well as introducing new ideas, interpretations and proofs. The authors begin by defining existentially closed groups, and summarizing some of the techniques that are basic to infinite group theory (e.g. the formation of free products with amalgamation and HNN-extensions). From this basis the theory is developed and many of the more recently discovered results are proved and discussed. The aim is to assist group theorists to find their way into a corner of their subject which has its own characteristic flavour, but which is recognizably group theory. Full Product DetailsAuthor: Graham Higman (Mathematical Institute, Mathematical Institute, University of Oxford) , Elizabeth Scott (Department of Mathematics, Department of Mathematics, The Australian National University, Canberra)Publisher: Oxford University Press Imprint: Clarendon Press Volume: 3 Dimensions: Width: 15.90cm , Height: 1.60cm , Length: 24.10cm Weight: 0.461kg ISBN: 9780198535430ISBN 10: 0198535430 Pages: 170 Publication Date: 30 June 1988 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: To order  Stock availability from the supplier is unknown. We will order it for you and ship this item to you once it is received by us. Table of ContentsNotation and conventions; Introduction; Centralizers and normalizers of subgroups; -homogeneous groups; Recursion theory; Applications of the Subgroup theorem; The Relative-Subgroup theorem; Games; Free products; First-order of existentially closed groups; Bibliography; Index.Reviews<br> The text is well written and accessible to anyone with some basic knowledge of group theory and logic. --American Mathematical Monthly<p><br> The text is well written and accessible to anyone with some basic knowledge of group theory and logic. --American Mathematical Monthly<br> The text is well written and accessible to anyone with some basic knowledge of group theory and logic. --American Mathematical Monthly 'Since the book was written, quite different developments have begun, concerning equations i groups... the Higman-Scott book should be a rich source of ideas for the new restricted theory.' London Mathematical Society Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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