
Accession Number : AD0741894
Title : The Word Problem and Power Problem in 1Relator 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 socalled 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