What do the Engel laws and positive laws have in common?
Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 7, pp. 175-183.

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The work is inspired by a question of R. Burns: What do the Engel laws and positive laws have in common that forces finitely generated, locally graded groups satisfying them to be nilpotent-by-finite? The answer is that these laws have the same so-called Engel construction.
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O. Macedońska. What do the Engel laws and positive laws have in common?. Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 7, pp. 175-183. http://geodesic.mathdoc.fr/item/FPM_2008_14_7_a14/

[1] Adyan S. I., Problema Bernsaida i tozhdestva v gruppakh, Nauka, M., 1975 | MR | Zbl

[2] Chernikov S. N., “Beskonechnye neabelevy podgruppy s usloviem invariantnosti dlya beskonechnykh neabelevykh podgrupp”, DAN SSSR, 194 (1970), 1280–1283 | Zbl

[3] Burns R. G., Macedońska O., Medvedev Yu., “Groups satisfying semigroup laws, and nilpotent-by-Burnside varieties”, J. Algebra, 195 (1997), 510–525 | DOI | MR | Zbl

[4] Burns R. G., Medvedev Yu., “Group laws implying virtual nilpotence”, J. Austral. Math. Soc., 74 (2003), 295–312 | DOI | MR | Zbl

[5] Groves J. R. J., “Varieties of soluble groups and a dichotomy of P. Hall”, Bull. Austral. Math. Soc., 5 (1971), 391–410 | DOI | MR | Zbl

[6] Gruenberg K. W., “Two theorems on Engel groups”, Math. Proc. Cambridge Philos. Soc., 49 (1953), 377–380 | DOI | MR | Zbl

[7] Kim Y. K., Rhemtulla A. H., “Weak maximality conditions and polycyclic groups”, Proc. Amer. Math. Soc., 123 (1995), 711–714 | DOI | MR | Zbl

[8] Milnor J., “Growth of finitely generated solvable groups”, J. Differential Geom., 2 (1968), 447–449 | MR | Zbl

[9] Neumann H., Varieties of Groups, Springer, Berlin, 1967 | MR | Zbl

[10] Ol'shanskii A. Yu., Storozhev A., “A group variety defined by a semigroup law”, J. Austral. Math. Soc. Ser. A, 60 (1996) | MR

[11] Point F., “Milnor identities”, Commun. Algebra, 24:12 (1996), 3725–3744 | DOI | MR | Zbl

[12] Rosset S., “A property of groups of non-exponential growth”, Proc. Amer. Math. Soc., 54 (1976), 24–26 | DOI | MR | Zbl

[13] Semple J. F., Shalev A., “Combinatorial conditions in residually finite groups. I”, J. Algebra, 157 (1993), 43–50 | DOI | MR | Zbl

[14] Wilson J. S., “Two-generator conditions for residually finite groups”, Bull. London Math. Soc., 23 (1991), 239–248 | DOI | MR | Zbl