On the word problem in the free quasigroups in the varieties of quasigroups isotopic to groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 20 (2015) no. 1, pp. 39-55.

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We consider the quasigroup varieties that are isotopic closures of the appropriate group varieties. We give the conditions for the word problem to be positively solvable simultaneously in the free algebras of the varieties of quasigroups and the corresponding groups.
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M. M. Glukhov. On the word problem in the free quasigroups in the varieties of quasigroups isotopic to groups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 20 (2015) no. 1, pp. 39-55. http://geodesic.mathdoc.fr/item/FPM_2015_20_1_a4/

[1] Belousov V. D., Osnovy teorii kvazigrupp i lup, Nauka, M., 1967 | MR

[2] Belousov V. D., “Uravnoveshennye tozhdestva v kvazigruppakh”, Matem. sb., 70(112):1 (1966), 55–97 | MR | Zbl

[3] Belyavskaya G. B., “$T$-kvazigruppy i tsentr kvazigruppy”, Mat. issled., 3, Shtiintsa, Kishinëv, 1989, 24–43 | MR

[4] Belyavskaya G. B., Tabarov A. Kh., “Kharakteristika lineinykh i alineinykh kvazigrupp”, Diskret. matem., 4:2 (1992), 142–147 | MR | Zbl

[5] Gvaramiya A. A., “Ob izotopii mezhdu gruppami i kvazigruppami”, IV Vsesoyuznyi simpozium po teorii grupp, Tezisy dokladov, M., 1984, 184–185

[6] Gvaramiya A. A., Aksiomatiziruemye klassy kvazigrupp i mnogosortnaya algebra, Dis. $\dots$ dokt. fiz.-mat. nauk, Novosibirsk, 1985

[7] Glukhov M. M., “$R$-mnogoobraziya kvazigrupp i lup”, Voprosy teorii kvazigrupp i lup, Kishinëv, 1971, 37–47 | Zbl

[8] Glukhov M. M., Gvaramiya A. A., “Reshenie osnovnykh algoritmicheskikh problem v nekotorykh klassakh kvazigrupp s tozhdestvami”, Sib. matem. zhurn., 10:2 (1969), 297–317 | Zbl

[9] Kurosh A. G., Lektsii po obschei algebre, Fizmatgiz, M., 1962 | MR

[10] Lemlein V. G., “O stroenii antiassotsiativnykh kvazilup”, Tezisy kr. nauch. soobschenii Mezhdunar. kongressa mat., Sektsiya 2, M., 1966, 46

[11] Lemlein V. G., “O stroenii antiassotsiativnykh kvazilup, porozhdënnykh konechnym chislom elementov”, Uchënye zapiski kafedry algebry i teorii chisel MGPI im. V. I. Lenina, 85, 1971, 68–79 | MR

[12] Maltsev A. I., “Tozhdestvennye sootnosheniya na mnogoobraziyakh kvazigrupp”, Matem. sb., 69(111):1 (1966), 3–12 | MR | Zbl

[13] Maltsev A. I., Algebraicheskie sistemy, Nauka, M., 1970 | MR

[14] Sokhatskii F. M., Assotsiaty i razlozheniya mnogomestnykh opreatsii, Dis. $\dots$ dokt. fiz.-mat. nauk, Kiev, 2006

[15] Tabarov A. Kh., Svobodnye lineinye kvazigruppy, Ne opublikovano, 2007

[16] Belyavskaya G. B., Tabarov A. H., “One-sided quasigroups”, Quasigroups Related Systems, 1:1 (1994), 1–7 | MR | Zbl

[17] Csacany B., “On the equivalence of certain classes of algebraic systems”, Acta Sci. Math. Szeged, 23 (1962), 46–57 | MR

[18] Drapal A., “On multiplication groups of relatively free quasigroups isotopic to Abelian groups”, Czech. Math. J., 55:130 (2005), 61–86 | DOI | MR | Zbl

[19] Evans T., “On multiplicative systems defined by generators and relations. I. Normal form theorem”, Proc. Cambridge Philos. Soc., 47 (1951), 637–649 | DOI | MR | Zbl

[20] Evans T., “The word problem for abstract algebras”, J. London Math. Soc., 28:1 (1951), 64–67 | DOI | MR

[21] Jezek J., Kepka T., “Quasigroups, isotopic to a group”, Comment. Math. Univ. Carolin., 16:1 (1975), 59–76 | MR | Zbl

[22] Kepka T., Nemec P., “$T$-quasigroups. I”, Acta Univ. Carolin. Math. Phys., 12:1 (1971), 31–39 | MR

[23] Kepka T., Nemec P., “$T$-quasigroups. II”, Acta Univ. Carolin. Math. Phys., 12:2 (1971), 39–49 | MR

[24] Sokhatsky F., “Description of isotopical closure of group isotopes”, Tretya mezhdunar. konf. po algebre, Sb. tezisov, Krasnoyarsk, 1993, 441