On the anticommutativity in Leibniz algebras
Algebra and discrete mathematics, Tome 26 (2018) no. 1, pp. 97-109.

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Lie algebras are exactly the anticommutative Leibniz algebras. In this article, we conduct a brief analysis of the approach to Leibniz algebras which based on the concept of the anti-center (Lie-center) and antinilpotency (Lie nilpotentency).
Mots-clés : Leibniz algebra, Lie algebra, center, Lie-center, anticenter, central series, anticentral series, Lie-central series.
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Leonid A. Kurdachenko; Nikolaj N. Semko; Igor Ya. Subbotin. On the anticommutativity in Leibniz algebras. Algebra and discrete mathematics, Tome 26 (2018) no. 1, pp. 97-109. https://geodesic-test.mathdoc.fr/item/ADM_2018_26_1_a9/

[1] V. A. Chupordya, L. A. Kurdachenko, I. Ya. Subbotin, “On some minimal Leibniz algebras”, Journal of Algebra and its Applications, 16 (2017) | DOI | MR

[2] J. M. Casas, E. Khmaladze, “On Lie-central extension of Leibniz algebra”, RACSAM, 111 (2017), 39–56 | DOI | MR | Zbl

[3] Ph. Hall, “Finite-by-nilpotent groups”, Proc. Cambridge Philos. Soc., 52 (1956), 611–616 | DOI | MR | Zbl

[4] V. V. Kirichenko, L. A. Kurdachenko, A. A. Pypka, I. Ya. Subbotin, “Some aspects of Leibniz algebra theory”, Algebra and Discrete Mathematics, 24:1 (2017), 113–145 | MR

[5] L. A. Kurdachenko, J. Otal, A. A. Pypka, “Relationships between factors of canonical central series of Leibniz algebras”, European Journal of Mathematics, 2 (2016), 565–577 | DOI | MR | Zbl

[6] L. A. Kurdachenko, I. Ya. Subbotin, “A brief history of an important classical theorem”, Advances in Group Theory and Applications, 2 (2016), 121–124 | MR | Zbl

[7] L. A. Kurdachenko, N. N. Semko, I. Ya. Subbotin, “From groups to Leibniz algebras: common approaches, parallel results”, Advances in Group Theory and Applications, 5 (2018), 1–31 | MR | Zbl

[8] B. H. Neumann, “Groups with finite classes of conjugate elements”, Proc. London Math. Soc., 1 (1951), 178–187 | DOI | MR | Zbl