The Power Problem for Groups with One Defining Relator

James McCool

doi:10.2307/2037985

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The Power Problem for Groups with One Defining Relator

James McCool

Year: 1971 Journal: Proceedings of the American Mathematical Society Vol: 28 (2)Pages: 427-427 Publisher: American Mathematical Society

DOI: 10.2307/2037985

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Abstract

It is proved that if G is a group with one defining relator, then the generalized word problem is solvable for every cyclic subgroup of G.This result enables the solution of the word problem for groups with one defining relator to be extended to a wider class of groups.

Keywords:

Mathematics Word problem (mathematics education) Word (group theory) Class (philosophy) Group (periodic table) Power (physics) Pure mathematics Combinatorics Algebra over a field Arithmetic Computer science Artificial intelligence Geometry

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Finite Group Theory Research

Physical Sciences → Mathematics → Discrete Mathematics and Combinatorics

Geometric and Algebraic Topology

Physical Sciences → Mathematics → Geometry and Topology

Advanced Graph Theory Research

Physical Sciences → Computer Science → Computational Theory and Mathematics

The Power Problem for Groups with One Defining Relator

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