Existentially Closed Groups

Erscheinungsjahr 1988
ISBN: 978-0-19-853543-0
Verlag: OUP Oxford

Buch, Englisch, Band 3, 170 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 409 g

Reihe: London Mathematical Society Monographs

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.

Autoren/Hrsg.

Higman, Graham

Scott, Elizabeth

Higman, G.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

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.