Abstract
1. A variety \( \mathfrak{N} \) of groups will be called positively definable if it can be defined by identical relations that do not include variables with negative powers.
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References
R. Baer, Factorization of n-soluble and n-nilpotent groups, Proc. Amer. Math. Soc. 4 (1953), no. 1, 15–26.
A.I. Malcev, Nilpotent semigroups, Ivanov. Gos. Ped. Inst. Uch. Zap. Fiz.-Mat. Nauki 4 (1953) 107–111.
A.I. Shirshov, On some groups which are nearly Engel, Algebra Logika 2 (1963) no. 5, 5–18.
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Shirshov, A.I. (2009). On Some Positively Definable Varieties of Groups. In: Bokut, L., Shestakov, I., Latyshev, V., Zelmanov, E. (eds) Selected Works of A.I. Shirshov. Contemporary Mathematicians. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8858-4_17
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