Geodesic
On systems of equations in a free group
Izvestiya. Mathematics, Tome 25 (1985) no. 1, pp. 115-162 
A. A. Razborov. On systems of equations in a free group. Izvestiya. Mathematics, Tome 25 (1985) no. 1, pp. 115-162. http://geodesic.mathdoc.fr/item/IM2_1985_25_1_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A description of the general solution of given bounded periodicity exponent is obtained for an arbitrary system of equations in a free group. On the basis of this result an algorithm is constructed that computes the rank of coefficient-free systems of equations. Bibliography: 7 titles.

[1] Makanin G. S., “Uravneniya v svobodnoi gruppe”, Izv. AN SSSR. Ser. matem., 46:6 (1982), 1199–1273 | MR | Zbl

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

[3] Lorents A. A., “O predstavlenii mnozhestv reshenii sistem uravnenii s odnim neizvestnym v svobodnykh gruppakh”, Dokl. AN SSSR, 178:2 (1968), 290–292 | Zbl

[4] Khmelevskii Yu. I., “Sistemy uravnenii v svobodnoi gruppe, 1, 2”, Izv. AN SSSR. Ser. matem., 35:6 (1971), 1237–1268 ; 36:1 (1972), 110–179

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

[6] Lindon R., Shupp P., Kombinatornaya teoriya grupp, Mir, M., 1980 | MR

[7] Makanin G. S., “Problema razreshimosti uravnenii v svobodnoi polugruppe”, Matem. sb., 103:2 (1977), 147–236 | MR | Zbl