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The solution of length three equations over groups

Published online by Cambridge University Press:  20 January 2009

James Howie
James Howie
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW
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Let G be a group, and let r = r(t) be an element of the free product G * 〈G〉 of G with the infinite cyclic group generated by t. We say that the equation r(t) = 1 has a solution in G if the identity map on G extends to a homomorphism from G * 〈G〉 to G with r in its kernel. We say that r(t) = 1 has a solution over G if G can be embedded in a group H such that r(t) = 1 has a solution in H. This property is equivalent to the canonical map from G to 〈G, t|r〉 (the quotient of G * 〈G〉 by the normal closure of r) being injective.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 26 , Issue 1 , February 1983 , pp. 89 - 96
Copyright
Copyright © Edinburgh Mathematical Society 1983

References

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