Geodesic
On elementary theories of integer linear groups
Izvestiya. Mathematics , Tome 59 (1995) no. 5, pp. 919-934.

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We study some restricted elementary theories of general, special and projective linear groups over the integers and discuss their algorithmic unsolvability. 
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V. G. Durnev. On elementary theories of integer linear groups. Izvestiya. Mathematics , Tome 59 (1995) no. 5, pp. 919-934. http://geodesic.mathdoc.fr/item/IM2_1995_59_5_a2/

[1] Maltsev A. I., “Ob elementarnykh svoistvakh lineinykh grupp”, Nekotorye problemy matematiki i mekhaniki, Novosibirsk, 1961, 110–132 | Zbl

[2] Adyan S. I., “O prostote periodicheskikh proizvedenii grupp”, DAN SSSR, 241:4 (1978), 745–748 | MR | Zbl

[3] Durnev V. G., Kazarin L. S., “Ob universalnykh teoriyakh nekotorykh grupp”, Vopr. teorii grupp i gomol. algebry, Yaroslavl, 1993, 3–12

[4] Suprunenko D. A., “O poryadke elementa gruppy tselochislennykh matrits”, DAN BSSR, 7:4 (1963), 221–223 | MR | Zbl

[5] Kargapolov M. I., Merzlyakov Yu. I., Osnovy teorii grupp, Nauka, M., 1982, S. 288 | MR | Zbl

[6] Kokseter G. S. M., Mozer U. O. Dzh., Porozhdayuschie elementy i opredelyayuschie sootnosheniya diskretnykh grupp, Nauka, M., 1980 | MR

[7] Merzlyakov Yu. I., “Lineinye gruppy”, Itogi nauki i tekhniki. Algebra. Topologiya. Geometriya, 16, VINITI, M., 1978, 35–90 | MR

[8] Dzheims G., Teoriya predstavlenii simmetricheskikh grupp, Mir, M., 1982 | MR

[9] Kertis Ch., Rainer I., Teoriya predstavlenii konechnykh grupp i assotsiativnykh algebr, Nauka, M., 1969 | MR

[10] Mennicke J. L., “Finite factor groups of the unimodular group”, Ann. Math., 81:1 (1963), 31–37 | DOI | MR

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

[12] Fadell E., Neuwirth L., “Configuration spaces”, Math. Scand., 10:1 (1962), 111–118 | MR | Zbl

[13] Zinde V. M., Gomomorfizmy gruppy Artina serii $B$ i $D$, Dep. v VINITI 6.06.77, No 242 2230–77, MGU, M., 1977

[14] Sacerdote G. S., “Almost all free products of groups have the same positive theory”, J. Algebra, 27:3 (1973), 475–485 | DOI | MR | Zbl

[15] Makanin G. S., “Razreshimost universalnoi i pozitivnoi teorii svobodnoi gruppy”, Izv. AN SSSR. Ser. matem., 48:4 (1984), 735–749 | MR | Zbl

[16] Ershov Yu. L., “Novye primery nerazreshimykh teorii”, Algebra i logika, 5:5 (1966), 37–48 | MR

[17] Slobodskoi A. M., “Universalnaya teoriya gruppy $\operatorname {GL}(3,\mathbb Z)$”, Algoritmicheskie voprosy algebraicheskikh sistem i EVM, Irkutsk, 1979, 200–217

[18] Maltsev A. I., “Ob odnom sootvetstvii mezhdu koltsami i gruppami”, Matem. sb., 50(92):3 (1960), 257–266 | MR | Zbl

[19] Durnev V. G., “O sistemakh uravnenii na svobodnykh nilpotentnykh gruppakh”, Vopr. teorii grupp i gomol. algebry, Yaroslavl, 1981, 66–69 | MR | Zbl

[20] Carter D., Keller G., “Elementary expressions for unimodular matrices”, Communications in Algebra, 12:4 (1984), 379–389 | DOI | MR | Zbl

[21] Slobodskoi A. M., “Nerazreshimost universalnoi teorii konechnykh grupp”, Algebra i logika, 20:2 (1981), 207–230 | MR | Zbl