An infinite simple Noetherian group without torsion
Izvestiya. Mathematics , Tome 15 (1980) no. 3, pp. 531-588.

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The well-known Baer conjecture on the “almost polycyclicity” of any Noetherian group is refuted; an example is constructed in terms of generators and defining relations. A complicated simultaneous induction on rank is based on a geometric interpretation of the deducibility of relations from defining relations. Bibliography: 6 titles.
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A. Yu. Ol'shanskii. An infinite simple Noetherian group without torsion. Izvestiya. Mathematics , Tome 15 (1980) no. 3, pp. 531-588. http://geodesic.mathdoc.fr/item/IM2_1980_15_3_a5/

[1] Baer R., “Noetherische Gruppen, I”, Math. Z., 66 (1956), 269–288 | DOI | MR | Zbl

[2] van Kampen E. R., “On some lemmas in the theory of groups”, Amer. J. Math., 55 (1933), 268–273 | DOI | MR | Zbl

[3] Lyndon R. C., “On Dehn's algorithm”, Math. Ann., 166 (1966), 208–228 | DOI | MR | Zbl

[4] Weinbaum C. M., “Visualizing the word problem, with an application to sixth groups”, Pacific. J. Math., 16 (1966), 557–578 | MR | Zbl

[5] Lyndon R. C., Schupp P. E., Combinatorial group theory, Springer-Verlag, Berlin, Heidelberg, New York, 1977 | MR | Zbl

[6] Novikov P. S., Adyan S. I., “O beskonechnykh periodicheskikh gruppakh, I, II, III”, Izv. AN SSSR. Seriya matem., 32:1, 2, 3 (1968), 212–244, 251–524, 709–731 | MR | Zbl