LINEAR ESTIMATES FOR SOLUTIONS OF QUADRATIC EQUATIONS IN FREE GROUPS-Reference-Cited by-同舟云学术

LINEAR ESTIMATES FOR SOLUTIONS OF QUADRATIC EQUATIONS IN FREE GROUPS

Published:2012-02 Issue:01 Volume:22 Page:1250004
ISSN:0218-1967
Container-title:International Journal of Algebra and Computation
language:en
Short-container-title:Int. J. Algebra Comput.

Author:

KHARLAMPOVICH OLGA¹,VDOVINA ALINA²

Affiliation:

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

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

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218196711006704

Reference19 articles.

1. Permutations and cubic graphs

2. Quadratic equations over free groups and free products

3. Powers as products of commutators

4. PRODUCTS OF COMMUTATORS AND PRODUCTS OF SQUARES IN A FREE GROUP

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