The solution of length four equations over groups

Authors:
Martin Edjvet and James Howie

Journal:
Trans. Amer. Math. Soc. **326** (1991), 345-369

MSC:
Primary 20E06; Secondary 20F05, 20F06

DOI:
https://doi.org/10.1090/S0002-9947-1991-1002920-5

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:
https://doi.org/10.1090/S0002-9947-1991-1002920-5

Article copyright:
© Copyright 1991
American Mathematical Society