HIERARCHIES OF COMPUTABLE GROUPS AND THE WORD PROBLEM,

Abstract

The Grzegorczyk hierarchy was extended to include the (partial) recursive functions, and sets of integers with decision problem restricted to any level of the hierarchy greater than four were constructed. Necessary and sufficient conditions for a finitely generated group to have its word problem solvable by a function at levels of the hierarchy greater than two were determined, and using the previously constructed sets, examples of finitely generated groups with decidable word problem restricted to levels greater than four were constructed. The work concluded with a discussion of eight unsolved problems. (Author)

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1964
Accession Number
AD0608036

Entities

People

  • Frank B. Cannonito

Organizations

  • Hughes Aircraft Company

Tags

DTIC Thesaurus Topics

  • Classification
  • Hierarchies
  • Recursive Functions

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.