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Book synopsis

Assuming only basic algebra and Galois theory, the book develops the method of "algebraic patching" to realize finite groups and, more generally, to solve finite split embedding problems over fields. The method succeeds over rational function fields of one variable over "ample fields". Among others, it leads to the solution of two central results in "Field Arithmetic": (a) The absolute Galois group of a countable Hilbertian pac field is free on countably many generators; (b) The absolute Galois group of a function field of one variable over an algebraically closed field $C$ is free of rank equal to the cardinality of $C$.

Book details

Book category Books in English Mathematics & science Mathematics Algebra

• Full title: Algebraic Patching
• Author: Moshe Jarden
• Language: English
• Binding: Hardback
• Number of pages: 292
• EAN: 9783642151279
• ISBN: 3642151272
• ID: 01656445
• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
• Weight: 582 g
• Dimensions: 239 × 160 × 22 mm
• Date of publishing: 01. January 2011

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