Book ChapterDOI
The Computability of Group Constructions, Part I
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In this paper, the authors discuss the computability of group constructions and discuss relative Grzegorczyk hierarchy and free products with amalgamation, and strong Britton extensions.Abstract:
Publisher Summary This chapter discusses the computability of group constructions. The chapter also discusses relative Grzegorczyk hierarchy and free products with amalgamation. A free product with amalgamation is a useful construction when dealing with decision problems in groups because intuitively the normal form theorem yields decision procedures for such products modulo the decision procedures for the groups and the amalgamated subgroups. The chapter discusses strong Britton extensions.read more
Citations
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Subrekursive Komplexität bei Gruppen
J. Avenhaus,Klaus Madlener +1 more
TL;DR: In this paper, it was shown that for two complexity classes K and K with K, there is no universal K-decidable f.p. group with generalized word problems.
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What are the gains of the theory of algorithms: Basis developments connected with the concept of algorithm and with its application in mathematics
Vladimir Uspensky,Alexei Semenov +1 more
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Infinitely generated subgroups of finitely presented groups. Part II
Journal ArticleDOI
Model-theoretic and algorithmic questions in group theory
TL;DR: A survey of results of an algorithmic nature can be found in this article, where model-theoretic methods and results in group theory are discussed, as well as a survey of group theory methods.
References
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Journal ArticleDOI
Computable algebra, general theory and theory of computable fields.
TL;DR: In this paper, the authors studied a blend of algebra and the theory of recursive functions for the problem of finding a solvable homomorphism in a finite set of generators of the word problem of a finitely generated group.
Journal ArticleDOI
Subgroups of Finitely Presented Groups
TL;DR: The main theorem of as discussed by the authors states that a finitely generated group can be embedded in a finite presented group if and only if it has a recursively enumerable set of defining relations.
Journal ArticleDOI
Primitive recursive functions
TL;DR: In this paper, the authors consider certain reductions in the recursion scheme for defining primitive recursive functions and refer to such functions simply as recursive functions, and also define some recursive functions which will be used.