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The descending chain condition on solution sets for systems of equations in groups

Published online by Cambridge University Press:  20 January 2009

M. H. Albert  and
J. Lawrence
M. H. Albert
Affiliation:
Department of Pure Mathematics, University of Waterloo, Canada
J. Lawrence
Affiliation:
Department of Pure Mathematics, University of Waterloo, Canada
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The Ehrenfeucht Conjecture [5] states that if Μ is a finitely generated free monoid with nonempty subset S, then there is a finite subset T⊂S (a “test set”) such that given two endomorphisms f and g on Μ, f and g agree on S if and only if they agree on T. In[4], the authors prove that the above conjecture is equivalent to the following conjecture: a system of equations in a finite number of unknowns in Μ is equivalent to a finite subsystem. Since a finitely generated free monoid embeds naturally into the free group with the same number of generators, it is natural to ask whether a free group of finite rank has the above property on systems of equations. A restatement of the question motivates the following.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 29 , Issue 1 , February 1986 , pp. 69 - 73
Copyright
Copyright © Edinburgh Mathematical Society 1986

References

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