Geodesic
A finitely presented solvable group with unsolvable word problem
Izvestiya. Mathematics, Tome 19 (1982) no. 1, pp. 151-169 
O. G. Kharlampovich. A finitely presented solvable group with unsolvable word problem. Izvestiya. Mathematics, Tome 19 (1982) no. 1, pp. 151-169. http://geodesic.mathdoc.fr/item/IM2_1982_19_1_a8/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper an example is constructed of a solvable group of length 3 with unsolvable word problem that is finitely presented in the class of all groups. Bibliography: 9 titles.

[1] Kourovskaya tetrad, 6-e izd., Novosibirsk, 1978

[2] Remeslennikov V. N., “Primer gruppy, konechno opredelennoi v mnogoobrazii $\mathfrak{A}^5$, s nerazreshimoi problemoi ravenstva slov”, Algebra i logika, 12:5 (1973), 577–602 | MR | Zbl

[3] Epanchintsev V. I., Kukin G. P., “Problema ravenstva v mnogoobrazii grupp, soderzhaschem $\mathfrak{R}_2\mathfrak{A}$”, Algebra i logika, 18:3 (1979), 259–285 | MR | Zbl

[4] Hall P., “On the finiteness of certain coluble groups”, Proc. London Math. Soc., 9 (1959), 592–622 | DOI | MR

[5] Slobodskoi A. M., “Nerazreshimost universalnoi teorii konechnykh grupp”, V Vsesoyuznaya konferentsiya po matematicheskoi logike, tezisy dokladov, Novosibirsk, 1979

[6] Kharlampovich O. G., “Universalnaya teoriya klassa konechnykh nilpotentnykh grupp nerazreshima”, V Vsesoyuznaya konferentsiya po matematicheskoi logike, tezisy dokladov, Novosibirsk, 1979

[7] Olshanskii A. Yu., “O probleme konechnogo bazisa tozhdestv v gruppakh”, Izv. AN SSSR. Ser. matem., 34:2 (1970), 376–384

[8] Kargapolov M. I., Merzlyakov Yu. I., Osnovy teorii grupp, Nauka, M., 1977 | MR | Zbl

[9] Maltsev A. I., Algoritmy i rekursivnye funktsii, Nauka, M., 1965 | MR