Geodesic
SCAP-subalgebras of Lie algebras
Czechoslovak Mathematical Journal, Tome 66 (2016) no. 4, pp. 1177-1184

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A subalgebra $H$ of a finite dimensional Lie algebra $L$ is said to be a $\rm SCAP$-subalgebra if there is a chief series $0=L_0\subset L_1\subset \ldots \subset L_t=L$ of $L$ such that for every $i=1,2,\ldots ,t$, we have $H+L_i=H+L_{i-1}$ or $H\cap L_i=H\cap L_{i-1}$. This is analogous to the concept of $\rm SCAP$-subgroup, which has been studied by a number of authors. In this article, we investigate the connection between the structure of a Lie algebra and its $\rm SCAP$-subalgebras and give some sufficient conditions for a Lie algebra to be solvable or supersolvable.
DOI : 10.1007/s10587-016-0317-3
Classification : 17B05, 17B30, 17B50
Keywords: Lie algebra; $\rm SCAP$-subalgebra; chief series; solvable; supersolvable 
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     title = {SCAP-subalgebras of {Lie} algebras},
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Chehrazi, Sara; Salemkar, Ali Reza. SCAP-subalgebras of Lie algebras. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 4, pp. 1177-1184. doi: 10.1007/s10587-016-0317-3

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