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

摘要

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)