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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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The solution of length four equations over groups
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by Martin Edjvet and James Howie PDF
Trans. Amer. Math. Soc. 326 (1991), 345-369 Request permission

Abstract:

Let $G$ be a group, $F$ the free group generated by $t$ and let $r(t) \in G \ast F$. The equation $r(t) = 1$ is said to have a solution over $G$ if it has a solution in some group that contains $G$. This is equivalent to saying that the natural map $G \to \langle G \ast F|r(t)\rangle$ is injective. There is a conjecture (attributed to M. Kervaire and F. Laudenbach) that injectivity fails only if the exponent sum of $t$ in $r(t)$ is zero. In this paper we verify this conjecture in the case when the sum of the absolute values of the exponent of $t$ in $r(t)$ is equal to four.
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Additional Information
  • © Copyright 1991 American Mathematical Society
  • 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