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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

On special linear characters of free groups of rank $ n\geq 4$


Author: Alice Whittemore
Journal: Proc. Amer. Math. Soc. 40 (1973), 383-388
MSC: Primary 20E35
MathSciNet review: 0322064
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Abstract: Let $ {F_n}$ be a free group of rank $ n$. In a recent paper R. Horowitz has shown that for $ n \leqq 3$ the ideal $ {I_n}$ in the ring of special linear characters of $ {F_n}$ consisting of those polynomials in the characters which vanish for all representations of $ {F_n}$ by subgroups of $ SL(2,C)$ is principal. In this paper the case $ n = 4$ is investigated; it is shown that for $ n > 3,{I_n}$ is not principal.


References [Enhancements On Off] (What's this?)

  • [1] R. Fricke and F. Klein, Vorlesungen über die Theorie der automorphen Functionen. Vol. 1, Teubner, Leipzig, 1897.
  • [2] Robert D. Horowitz, Characters of free groups represented in the two-dimensional special linear group, Comm. Pure Appl. Math. 25 (1972), 635–649. MR 0314993 (47 #3542)
  • [3] W. Magnus, A. Karass and D. Solitar, Combinatorial group theory: Presentations of groups in terms of generators and relations, Pure and Appl. Math., vol. 13, Interscience, New York, 1966. MR 34 #7617.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0322064-X
PII: S 0002-9939(1973)0322064-X
Keywords: Special linear characters, character manifold, automorphism group of a free group
Article copyright: © Copyright 1973 American Mathematical Society