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Lie perfect, Lie central extension and generalization of nilpotency in multiplicative Lie algebras
Czechoslovak Mathematical Journal, Tome 74 (2024) no. 1, pp. 283-299
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This paper aims to introduce and explore the concept of Lie perfect multiplicative Lie algebras, with a particular focus on their connections to the central extension theory of multiplicative Lie algebras. The primary objective is to establish and provide proof for a range of results derived from Lie perfect multiplicative Lie algebras. Furthermore, the study extends the notion of Lie nilpotency by introducing and examining the concept of local nilpotency within multiplicative Lie algebras. The paper presents an innovative adaptation of the Hirsch-Plotkin theorem specifically tailored for multiplicative Lie algebras.\looseness -1
This paper aims to introduce and explore the concept of Lie perfect multiplicative Lie algebras, with a particular focus on their connections to the central extension theory of multiplicative Lie algebras. The primary objective is to establish and provide proof for a range of results derived from Lie perfect multiplicative Lie algebras. Furthermore, the study extends the notion of Lie nilpotency by introducing and examining the concept of local nilpotency within multiplicative Lie algebras. The paper presents an innovative adaptation of the Hirsch-Plotkin theorem specifically tailored for multiplicative Lie algebras.\looseness -1
DOI : 10.21136/CMJ.2024.0261-23
Classification : 17A99, 19G24, 20A99, 20F19
Keywords: multiplicative Lie algebra; commutator; nilpotent group; perfect group; central extensions 
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Singh, Dev Karan; Pandey, Mani Shankar; Kumar, Shiv Datt. Lie perfect, Lie central extension and generalization of nilpotency in multiplicative Lie algebras. Czechoslovak Mathematical Journal, Tome 74 (2024) no. 1, pp. 283-299. doi: 10.21136/CMJ.2024.0261-23

[1] Bak, A., Donadze, G., Inassaridze, N., Ladra, M.: Homology of multiplicative Lie rings. J. Pure Appl. Algebra 208 (2007), 761-777. | DOI | MR | JFM

[2] Donadze, G., Inassaridze, N., Ladra, M., Vieites, A. M.: Exact sequences in homology of multiplicative Lie rings and a new version of Stallings' theorem. J. Pure Appl. Algebra 222 (2018), 1786-1802. | DOI | MR | JFM

[3] Donadze, G., Ladra, M.: More on five commutator identities. J. Homotopy Relat. Struct. 2 (2007), 45-55. | MR | JFM

[4] Ellis, G. J.: On five well-known commutator identities. J. Aust. Math. Soc., Ser. A 54 (1993), 1-19. | DOI | MR | JFM

[5] Lal, R.: Algebra 2. Linear Algebra, Galois Theory, Representation Theory, Group Extensions and Schur Multiplier. Infosys Science Foundation Series. Springer, Singapore (2017). | DOI | MR | JFM

[6] Lal, R., Upadhyay, S. K.: Multiplicative Lie algebras and Schur multiplier. J. Pure Appl. Algebra 223 (2019), 3695-3721. | DOI | MR | JFM

[7] Pandey, M. S., Lal, R., Upadhyay, S. K.: Lie commutator, solvability and nilpotency in multiplicative Lie algebras. J. Algebra Appl. 20 (2021), Article ID 2150138, 11 pages. | DOI | MR | JFM

[8] Pandey, M. S., Upadhyay, S. K.: Theory of extensions of multiplicative Lie algebras. J. Lie Theory 31 (2021), 637-658. | MR | JFM

[9] Pandey, M. S., Upadhyay, S. K.: Classification of multiplicative Lie algebra structures on a finite group. Colloq. Math. 168 (2022), 25-34. | DOI | MR | JFM

[10] Point, F., Wantiez, P.: Nilpotency criteria for multiplicative Lie algebras. J. Pure Appl. Algebra 111 (1996), 229-243. | DOI | MR | JFM

[11] Robinson, D. J. S.: A Course in the Theory of Groups. Graduate Texts in Mathematics 80. Springer, New York (1996). | DOI | MR | JFM

[12] Walls, G. L.: Multiplicative Lie algebras. Turk. J. Math. 43 (2019), 2888-2897. | DOI | MR | JFM

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