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Algorithmic and Combinatorial Algebra : MATHEMATICS AND ITS APPLICATIONS (KLUWER ) - L. A. Bokut'

Algorithmic and Combinatorial Algebra



Published: 31st May 1994
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Even three decades ago, the words 'combinatorial algebra' contrasting, for in­ stance, the words 'combinatorial topology,' were not a common designation for some branch of mathematics. The collocation 'combinatorial group theory' seems to ap­ pear first as the title of the book by A. Karras, W. Magnus, and D. Solitar [182] and, later on, it served as the title of the book by R. C. Lyndon and P. Schupp [247]. Nowadays, specialists do not question the existence of 'combinatorial algebra' as a special algebraic activity. The activity is distinguished not only by its objects of research (that are effectively given to some extent) but also by its methods (ef­ fective to some extent). To be more exact, we could approximately define the term 'combinatorial algebra' for the purposes of this book, as follows: So we call a part of algebra dealing with groups, semi groups , associative algebras, Lie algebras, and other algebraic systems which are given by generators and defining relations {in the first and particular place, free groups, semigroups, algebras, etc. )j a part in which we study universal constructions, viz. free products, lINN-extensions, etc. j and, finally, a part where specific methods such as the Composition Method (in other words, the Diamond Lemma, see [49]) are applied. Surely, the above explanation is far from covering the full scope of the term (compare the prefaces to the books mentioned above).

Composition Method for Associative Algebrasp. 1
Free Lie Algebrasp. 53
The Composition Method in the Theory of Lie Algebrasp. 105
Amalgamated Products of Lie Algebrasp. 141
The Problem of Endomorph Reducibility and Relatively Free Groups with the Word Problem Unsolvablep. 177
The Constructive Method in the Theory of HNN-extensions. Groups with Standard Normal Formp. 209
The Constructive Method for HNN-extensions and the Conjugacy Problem for Novikov-Boone Groupsp. 237
Appendix 1 Calculations in Free Groupsp. 315
Appendix 2 Algorithmic Properties of the Wreath Products of Groupsp. 325
Appendix 3 Survey of the Theory of Absolutely Free Algebrasp. 335
Bibliographyp. 349
Indexp. 380
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792323136
ISBN-10: 0792323130
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 384
Published: 31st May 1994
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 25.4 x 17.15  x 2.54
Weight (kg): 0.86