The Elementary Theory of Groups is popular PDF and ePub book, written by Benjamin Fine in 2014-10-29, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, The Elementary Theory of Groups can be Read Online from any device for your convenience.
The Elementary Theory of Groups Book PDF Summary
After being an open question for sixty years the Tarski conjecture was answered in the affirmative by Olga Kharlampovich and Alexei Myasnikov and independently by Zlil Sela. Both proofs involve long and complicated applications of algebraic geometry over free groups as well as an extension of methods to solve equations in free groups originally developed by Razborov. This book is an examination of the material on the general elementary theory of groups that is necessary to begin to understand the proofs. This material includes a complete exposition of the theory of fully residually free groups or limit groups as well a complete description of the algebraic geometry of free groups. Also included are introductory material on combinatorial and geometric group theory and first-order logic. There is then a short outline of the proof of the Tarski conjectures in the manner of Kharlampovich and Myasnikov.
Detail Book of The Elementary Theory of Groups PDF
- Author : Benjamin Fine
- Release : 29 October 2014
- Publisher : Walter de Gruyter GmbH & Co KG
- ISBN : 9783110382570
- Genre : Mathematics
- Total Page : 333 pages
- Language : English
- PDF File Size : 14,9 Mb
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