UID:
almahu_9949462257802882
Format:
1 online resource (307 p.)
ISBN:
9783110342031
,
9783110494969
Series Statement:
De Gruyter Expositions in Mathematics , 60
Content:
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.
Note:
Frontmatter --
,
Preface --
,
Contents --
,
1 Group theory and logic: introduction --
,
2 Combinatorial group theory --
,
3 Geometric group theory --
,
4 First order languages and model theory --
,
5 The Tarski problems --
,
6 Fully residually free groups I --
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7 Fully residually free groups II --
,
8 Algebraic geometry over groups --
,
9 The solution of the Tarski problems --
,
10 On elementary free groups and extensions --
,
11 Discriminating and squarelike groups --
,
References --
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Index
,
Issued also in print.
,
Mode of access: Internet via World Wide Web.
,
In English.
In:
DG Expositions in Mathematics Backlist eBook Package, De Gruyter, 9783110494969
In:
DGBA Backlist Complete English Language 2000-2014 PART1, De Gruyter, 9783110238570
In:
DGBA Backlist Mathematics 2000-2014 (EN), De Gruyter, 9783110238471
In:
DGBA Mathematics - 2000 - 2014, De Gruyter, 9783110637205
In:
EBOOK PACKAGE Complete Package 2014, De Gruyter, 9783110369526
In:
EBOOK PACKAGE Mathematics, Physics 2014, De Gruyter, 9783110370355
Additional Edition:
ISBN 9783110382570
Additional Edition:
ISBN 9783110341997
Language:
English
DOI:
10.1515/9783110342031
URL:
https://doi.org/10.1515/9783110342031
URL:
https://www.degruyter.com/isbn/9783110342031
