The solution of length four equations over groups
Authors:
Martin Edjvet and James Howie
Journal:
Trans. Amer. Math. Soc. 326 (1991), 345369
MSC:
Primary 20E06; Secondary 20F05, 20F06
MathSciNet review:
1002920
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Abstract: Let be a group, the free group generated by and let . The equation is said to have a solution over if it has a solution in some group that contains . This is equivalent to saying that the natural map is injective. There is a conjecture (attributed to M. Kervaire and F. Laudenbach) that injectivity fails only if the exponent sum of in is zero. In this paper we verify this conjecture in the case when the sum of the absolute values of the exponent of in is equal to four.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947199110029205
PII:
S 00029947(1991)10029205
Article copyright:
© Copyright 1991
American Mathematical Society
