A DESCRIPTION OF SOLUTIONS OF QUADRATIC EQUATIONS IN HYPERBOLIC GROUPS-Reference-Cited by-同舟云学术

A DESCRIPTION OF SOLUTIONS OF QUADRATIC EQUATIONS IN HYPERBOLIC GROUPS

Published:1992-09 Issue:03 Volume:02 Page:237-274
ISSN:0218-1967
Container-title:International Journal of Algebra and Computation
language:en
Short-container-title:Int. J. Algebra Comput.

Author:

GRIGORCHUK R.I.¹,LYSIONOK I.G.²

Affiliation:

1. Moscow Inst. of Railway Transport Engineers, Obraztsov Street 15, Moscow 101475, Russia

2. Steklov Mathematical Institute, Vavilova Str. 42, Moscow 117966 17966 GSP-1, Russia

Abstract

A description is given for the set of solutions of a quadratic equation in a hyperbolic group. It consists of a finite set of parametric solutions of the equation which generates all solutions by the action of a group which may be interpreted as a special mapping class group of a compact surface.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218196792000153

Cited by 9 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Quadratic equations in metabelian Baumslag–Solitar groups;International Journal of Algebra and Computation;2023-08-21

2. The complexity of solution sets to equations in hyperbolic groups;Israel Journal of Mathematics;2021-10

3. Quadratic equations in hyperbolic groups are NP-complete;Transactions of the American Mathematical Society;2017-02-13

4. LINEAR ESTIMATES FOR SOLUTIONS OF QUADRATIC EQUATIONS IN FREE GROUPS;International Journal of Algebra and Computation;2012-02

5. Asymptotic invariants, complexity of groups and related problems;Bulletin of Mathematical Sciences;2011-03-29