Groups with Solvable Word Problems (Classic Reprint) - Couverture souple

Semeniuk, Christine

Couverture souple

ISBN 10 : 1330197348 ISBN 13 : 9781330197349

Editeur : Forgotten Books, 2018

A propos du livre

Présentation de l'éditeur

This paper considers two aspects of the word problem for groups: first, some similarities between derivations from the relations of a group and proofs from a set of axioms in logic, and second, the computational difficulty of word problems and the problem of constructing groups with solvable word problems of some preassigned degree of difficulty. Given a presentation of a group in terms of generators and relations, we define two words on the generators to be equal if and only if one can be transformed into the other in a finite number of steps using the relations of the group. Defining equality in a group as derivability from a set of axioms suggests formulating the word problem for a group as the derivability problem for a formal system. The system we choose is equational logic. We show that there exist some striking analogies between results from logic and results about groups: nontrivial groups correspond to consistent systems, groups with solvable word problem to decidable systems, and simple groups to complete systems. This suggests that results about formal systems could be used to obtain results about decidability in groups. A group has word problem in level of the Grzegorczyk hierarchy if the running time of the algorithm solving the word problem is in .G roups having word problem solvable in levels s(n 2) of the Grzegorczyk hierarchy are given. The groups are constructed using a standard procedure of constructing a group given the presentation of a semigroup. Semigroups are constructed following J. Robinson smethod of functional equations: the semigroups are decidable systems of functional equations which define functions in .T his technique for constructing semigroups is particularly elegant, for it has the advantage of exhibiting the semigroup as a concrete system. We show that if the semigroup has word problem ins (and not lower) ,then the result
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Détails de l'édition

• Éditeur: Forgotten Books
• Date d'édition: 2018
• Langue: anglais
• ISBN 10: 1330197348
• ISBN 13: 9781330197349
• Reliure: Broché
• Nombre de pages: 90
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