The Word Problem and Power Problem in 1-Relator Groups is Elementary,

Abstract

The work extends the study of the solvability level of the word problem in finitely generated groups with respect to the Grzegorczyk hierarchy. In particular, the paper presents a proof of the elementary decidability of the word problem, order problem, and power problem in finitely generated groups presentable on 1 defining relator. The magnus theorem proof is used to show that the algorithm giving the solution to the word problem can always be realized as a function in the third level of the Grzegorczyk hierarchy. These are the so-called Kalmar elementary functions. (Author)

Document Details

Document Type
Technical Report
Publication Date
May 04, 1972
Accession Number
AD0741894

Entities

People

  • F. B. Cannonito
  • R. W. Gatterdam

Organizations

  • University of California, Irvine

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Behavior And Behavior Mechanisms
  • Behavioral Disciplines And Activities
  • Behavioral Sciences
  • Classification
  • Continents
  • Cooperation
  • Geographic Regions
  • Group Dynamics
  • Hierarchies
  • Mathematics
  • North America
  • Wisconsin

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.