Solution of the Word Problem for Certain Types of Groups I
- 1 December 1956
- journal article
- research article
- Published by Cambridge University Press (CUP) in Proceedings of the Glasgow Mathematical Association
- Vol. 3 (1) , 45-54
- https://doi.org/10.1017/s2040618500033426
Abstract
The main result of this series of papers is a theorem on the free product of groups (Theorem 1) which formed part of a doctoral thesis. This theorem has an immediate application to the word problem (Theorem 2). Usually the word problem refers to a finite system of generators and a finite number of defining relations, but in this context it is more natural to allow an infinite number of generators and defining relations. This (infinite) word problem is not solvable in general (Example 2).Keywords
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