# Accession Number:

## AD0741894

# Title:

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

# Descriptive Note:

# Corporate Author:

## CALIFORNIA UNIV IRVINE DEPT OF MATHEMATICS

# Personal Author(s):

# Report Date:

## 1972-05-04

# Pagination or Media Count:

## 17.0

# 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:

# Subject Categories:

- Theoretical Mathematics