Geodesic
On equations in free groups with restrictions on solutions
Čebyševskij sbornik, Tome 11 (2010) no. 3, pp. 88-97.

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

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V. G. Durnev; O. V. Zetkina. On equations in free groups with restrictions on solutions. Čebyševskij sbornik, Tome 11 (2010) no. 3, pp. 88-97. http://geodesic.mathdoc.fr/item/CHEB_2010_11_3_a8/

[1] Durnev V. G., “Ob uravneniyakh na svobodnykh polugruppakh i gruppakh”, Matem. zametki, 16:5 (1974), 717–724 | MR

[2] Durnev V. G., “O probleme razreshimosti dlya uravnenii s odnim koeffitsientom”, Matem. zametki, 59:6 (1996), 832–845 | MR | Zbl

[3] Kourovskaya tetrad, 11-e izd., dop., Novosibirsk, 1990

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

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

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

[7] Makanin G. S., “Universalnaya teoriya i pozitivnaya teoriya svobodnoi gruppy”, Izv. AN SSSR. Ser. matem., 48:4 (1984), 735–749 | MR

[8] Maltsev A. I., “Ob uravnenii $zxyx^{-1}y^{-1}z^{-1} = aba^{-1}b^{-1}$ v svobodnoi gruppe”, Algebra i logika, 1:5 (1962), 45–50 | MR

[9] Malkhasyan A. Sh., “O razreshimosti v podgruppakh uravnenii v svobodnoi gruppe”, Prikladnaya matematika, 1986, no. 2, 42–47 | MR | Zbl

[10] Matiyasevich Yu. V., “Diofantovost perechislimykh mnozhestv”, Dokl. AN SSSR, 130:3 (1970), 495–498

[11] Merzlyakov Yu. I., “Pozitivnye formuly na svobodnykh gruppakh”, Algebra i logika, 5:4 (1966), 25–42 | MR | Zbl

[12] Razborov A. A., “O sistemakh uravnenii v svobodnoi gruppe”, Izv. AN SSSR. Ser. matem., 48:4 (1984), 779–832 | MR

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

[14] Birman J. S., Braids, links and mapping class groups, Ann. of Math. Studies, 82, Princeton University Press, Princeton, 1974 | MR

[15] Diekert V., Makanin's Algorithm for Solving Word Equations with Regular Constraints, Report No 1998/02, Fakultat Informatik. Universitat Stuttgart, 1998 (Preliminary version of the chapter in M. Lothaire, Algebraic Combinatorics on Words)

[16] Gassner B. J., “On braid groups”, Abh. Math. Sem. Univ. Hamburg, 25 (1961), 10–22 | MR | Zbl

[17] Edmunds C. C., “On the endomorphisms problem for free group”, Com. Algebra, 1975, no. 3, 7–20 | MR

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

[19] Tarski A., Mostowski A., Robinson R. M., Undecidable theories, N.Y., 1953, XI+98 pp. | Zbl

[20] Schupp P. E., “On the substitution problem for free groups”, Proc. Amer. Math. Soc., 23 (1969), 421–423 | MR | Zbl