Defining relations and algorithmic problems for groups and semigroups
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Defining relations and algorithmic problems for groups and semigroups by S I. Adyan

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Published by American Mathematical Society in Providence .
Written in English


Book details:

Edition Notes

Translation of: Opredelyayushchie sootnosheniya i algoritmicheskie problemy dlya grupp i polgrupp. Moskva: Nauka, 1966.

Statementby S.I. Adjan ; translated from theRussian by M. Greendlinger.
SeriesTrudy -- 85.
ID Numbers
Open LibraryOL19583590M

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Algorithmic Problems in Groups and Semigroups Jorge Almeida, Benjamin Steinberg (auth.), Jean-Camille Birget, Stuart Margolis, John Meakin, Mark Sapir (eds.) This volume contains papers which are based primarily on talks given at an inter­ national conference on Algorithmic Problems in Groups and Semigroups held at the University of Nebraska-Lincoln from May ll- Defining relations and algorithmic problems for groups and semigroups S. I. Adian Full text: PDF file ( kB) English version: Proceedings of the Steklov Institute of Mathematics, , 85, 1– Bibliographic databases: UDC: 51(). Get this from a library! Algorithmic problems in groups and semigroups. [J -C Birget;] -- "The stimulus for this volume was provided by the international conference on Algorithmic Problems in Groups and Semigroups, held in May of at the University of Nebraska-Lincoln."--BOOK JACKET. The purpose of the conference was to bring together researchers with interests in algorithmic problems in group theory, semigroup theory and computer science. A particularly useful feature of this conference was that it provided a framework for exchange of ideas between the research communities in semigroup theory and group theory, and several.

  In Max Dehn formulated three main algorithmic problems for groups presented by defining relations: Word problem, Conjugacy problem and Isomorphism problem. Two years later A. Thue formulated the Word problem for semigroups presented by defining relations (Thue systems).   The paper presents a detailed survey of results concerning the main decision problems of group theory and semigroup theory, including the word problem, the isomorphism problem, recognition problems, and other algorithmic questions related to them. on which the insolubility of the word problem for semigroups is based. in the class of. 2 Submonoids of groups It is perhaps the case that group theorists encounter semigroups (or monoids) most naturally as submonoids of groups. For example, if Pis a submonoid of a group Gsuch that P∩P−1 = {1}, then the relation ≤P on Gdefined by g≤P hiff g−1h∈ P is a left invariant partial order on G. 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.

This is a survey of using Minsky machines to study algorithmic problems in semigroups, groups and other algebraic systems. Defining relations correspond to pairs of equivalent short paths on.   The concept of presentation of semigroups (G,R), G an alphabet or set of generators, R a set of defining relations, is extended t o presentation of monoids (Q,R), Q a set of existing monomials (letters included) and R a set of defining relations among members of Q. Monoids themselves are presentations of themselves, as well * For a first.   No algorithm for solving the word problem in the general case has yet () been found, not even for semi-groups with a single defining relation; it was only constructed for irreducible defining relations. The algorithm solving the word problem for groups with one defining relation dates a long time back, but even for two such relations the. Computer science is the study of problems, problem-solving, and the solutions that come out of the problem-solving process. Given a problem, a computer scientist’s goal is to develop an algorithm, a step-by-step list of instructions for solving any instance of the problem that might arise.