Об уравнениях в свободных группах, разрешенных относительно неизвестных, с ограничениями на решения
Čebyševskij sbornik, Tome 13 (2012) no. 1, pp. 63-80.

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

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V. G. Durnev; O. V. Zetkina. Об уравнениях в свободных группах, разрешенных относительно неизвестных, с ограничениями на решения. Čebyševskij sbornik, Tome 13 (2012) no. 1, pp. 63-80. http://geodesic.mathdoc.fr/item/CHEB_2012_13_1_a6/

[1] Tarski A., Mostowski A., Robinson R. M., Undecidable theories, N. Y., 1953 | 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”, Doklady AN SSSR, 178:2 (1968), 290–292 | Zbl

[4] “One-variable equations in free groups”, Proc. Amer. Math. Soc., 19 (1968), 912–918 | DOI | MR | Zbl

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

[6] Makanin G. S., “Uravneniya v svobodnoi gruppe”, 46, no. 6, 1982, 1199–1273 | MR | Zbl

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

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

[9] Razborov A. A., “O sistemakh uravnenii v svobodnoi gruppe”, Izvestiya AN SSSR. Seriya matematicheskaya, 48:4 (1984), 779–832 | MR

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

[11] Birman J. S., Braids, links and mapping class groups, Ann.of Math. Studies No 82, Princeton University Press, Princeton, 1974 | MR

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

[13] Malkhasyan A. Sh., “O razreshimosti v podgruppakh uravnenii v svobodnoi gruppe”, Prikladnaya matematika, Sbornik, v. 2, 1986, 42–47 | Zbl

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

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

[16] 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

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

[18] Edmunds C. C., “On the endomorphisms problem for free group”, Com. Algebra, 3 (1975), 7–20 | DOI | MR

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

[20] Vdovina A. A., “Proizvedenie kommutatorov i kvadratov v svobodnoi gruppe”, Tretya mezhdunarodnaya konferentsiya po algebre, Sbornik tezisov, Izd-vo. KrGU, Krasnoyarsk, 1993, 66–67

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

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

[23] Krouell R., Foks R., Vvedenie v teoriyu uzlov, Mir, M., 1967 | MR

[24] Bormotov D., Gilman R., Myasnikov A., “Solving one-variable equation in free groups”, J. Group Theory, 12:2 (2009), 317–330 | DOI | MR | Zbl

[25] Kargapolov M. I., Remeslennikov V. N., “Problema sopryazhennosti dlya svobodnykh razreshimykh grupp”, Algebra i logika, 5:6 (1966), 15–26 | MR

[26] Krasnikov A. F., “O porozhdayuschikh elementakh grupp vida $F/[N, N]$”, Matem. zametki, 24:2 (1978), 167–173 | MR | Zbl

[27] Remeslennikov V. N., Sokolov V. G., “Nekotorye svoistva vlozheniya Magnusa”, Algebra i logika, 9:5 (1970), 556–578 | MR

[28] Maltsev A. I., “O svobodnykh razreshimykh gruppakh”, Doklady AN SSSR, 130:3 (1960), 495–498

[29] Neiman Kh., Mnogoobraziya grupp, Mir, M., 1969 | MR