Geodesic
Parametric equations in free groups
Matematičeskie zametki, Tome 58 (1995) no. 4, pp. 569-581 
Yu. I. Ozhigov. Parametric equations in free groups. Matematičeskie zametki, Tome 58 (1995) no. 4, pp. 569-581. http://geodesic.mathdoc.fr/item/MZM_1995_58_4_a8/
@article{MZM_1995_58_4_a8,
     author = {Yu. I. Ozhigov},
     title = {Parametric equations in free groups},
     journal = {Matemati\v{c}eskie zametki},
     pages = {569--581},
     year = {1995},
     volume = {58},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1995_58_4_a8/}
}
TY  - JOUR
AU  - Yu. I. Ozhigov
TI  - Parametric equations in free groups
JO  - Matematičeskie zametki
PY  - 1995
SP  - 569
EP  - 581
VL  - 58
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/MZM_1995_58_4_a8/
LA  - ru
ID  - MZM_1995_58_4_a8
ER  - 
%0 Journal Article
%A Yu. I. Ozhigov
%T Parametric equations in free groups
%J Matematičeskie zametki
%D 1995
%P 569-581
%V 58
%N 4
%U http://geodesic.mathdoc.fr/item/MZM_1995_58_4_a8/
%G ru
%F MZM_1995_58_4_a8

Voir la notice de l'article provenant de la source Math-Net.Ru

We introduce the notion of a parametric equation in a free group; this is an equation containing natural parameters as exponents and a system of linear Diophantine equations relating these exponents. For these equations, we introduce elementary transformations that are necessary for the description of general solutions of ordinary equations in a free group. We prove that it is possible to linearize any relation among parameters that appears in the course of transformations of the given equation.

[1] Lyndon R. C., “Equations in free groups”, Trans. Amer. Math. Soc., 96 (1960), 445–457 | DOI | MR | Zbl

[2] Ozhigov Yu. I., “Uravneniya s dvumya neizvestnymi v svobodnoi gruppe”, DAN SSSR, 268:4 (1983), 808–814 | MR

[3] Razborov A. A., O sistemakh uravnenii v svobodnoi gruppe, Diss. ...kand. fiz.-mat. nauk, MGU, M., 1987