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Existentially Closed Groups : London Mathematical Society Monographs - Graham Higman

Existentially Closed Groups

London Mathematical Society Monographs


Published: 30th June 1988
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This 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.

'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

Notation 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.

ISBN: 9780198535430
ISBN-10: 0198535430
Series: London Mathematical Society Monographs
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 170
Published: 30th June 1988
Publisher: Oxford University Press
Country of Publication: GB
Dimensions (cm): 24.1 x 15.9  x 1.6
Weight (kg): 0.47