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LINEAR ESTIMATES FOR SOLUTIONS OF QUADRATIC EQUATIONS IN FREE GROUPS

OLGA KHARLAMPOVICH

Department of Mathematics and Statistics, Hunter College, CUNY, 695 Park Avenue, New York, NY 10065, USA

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and

ALINA VDOVINA

School of Mathematics and Statistics, Newcastle University, Newcastle-upon-Tyne, NE17RU, UK

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https://doi.org/10.1142/S0218196711006704Cited by:4 (Source: Crossref)

Abstract

We prove that in a free group the length of the value of each variable in a minimal solution of a standard quadratic equation is bounded by 2s for an orientable equation and by 12s⁴ for a non-orientable equation, where s is the sum of the lengths of the coefficients.

Keywords:

AMSC: 20F10

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