| Algebraic Patching Contributor(s): Jarden, Moshe (Author) |
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ISBN: 3642151272 ISBN-13: 9783642151279 Publisher: Springer OUR PRICE: $52.24 Product Type: Hardcover - Other Formats Published: January 2011 |
| Additional Information |
| BISAC Categories: - Mathematics | Algebra - General - Mathematics | Group Theory - Mathematics | Algebra - Abstract |
| Dewey: 512 |
| Series: Springer Monographs in Mathematics |
| Physical Information: 0.85" H x 6.63" W x 9.6" (1.26 lbs) 292 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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 $C$. |