Accession Number : AD0741894

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

Corporate Author : CALIFORNIA UNIV IRVINE DEPT OF MATHEMATICS

Personal Author(s) : Cannonito,F. B. ; Gatterdam,R. W.

Report Date : 04 MAY 1972

Pagination or Media Count : 17

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)

Descriptors :   (*GROUPS(MATHEMATICS), MATHEMATICAL LOGIC), ALGEBRA, SET THEORY, RECURSIVE FUNCTIONS, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE