Mathematics and Its Applications

By: L.A. Bokut', G.P.. Kukin

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Hardcover | 31 May 1994

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404 Pages

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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).

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Non-Fiction Mathematics Combinatorics & Graph Theory Algebra Computing & I.T.Computer Programming & Software Development Algorithms & Data Structures Applied Mathematics Number Theory Gardening

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

Mathematics and Its Applications

At a Glance

Hardcover

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How to return your order

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