Geodesic
C-Supplemented Subalgebras of Lie Algebras
Journal of Lie theory, Tome 18 (2008) no. 3, pp. 717-724

Voir la notice de l'article provenant de la source Heldermann Verlag

A subalgebra $B$ of a Lie algebra $L$ is c-{\it supplemented} in $L$ if there is a subalgebra $C$ of $L$ with $L = B + C$ and $B \cap C \leq B_L$, where $B_L$ is the core of $B$ in $L$. This is analogous to the corresponding concept of a c-supplemented subgroup in a finite group. We say that $L$ is c-{\it supplemented} if every subalgebra of $L$ is c-supplemented in $L$. We give here a complete characterisation of c-supplemented Lie algebras over a general field.
Classification : 17B05, 17B20, 17B30, 17B50
Mots-clés : Lie algebras, c-supplemented subalgebras, completely factorisable algebras, Frattini ideal, subalgebras of codimension one 
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     author = {D. A. Towers },
     title = {C-Supplemented {Subalgebras} of {Lie} {Algebras}},
     journal = {Journal of Lie theory},
     pages = {717--724},
     publisher = {mathdoc},
     volume = {18},
     number = {3},
     year = {2008},
     url = {http://geodesic.mathdoc.fr/item/JLT_2008_18_3_JLT_2008_18_3_a13/}
}
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D. A. Towers . C-Supplemented Subalgebras of Lie Algebras. Journal of Lie theory, Tome 18 (2008) no. 3, pp. 717-724. http://geodesic.mathdoc.fr/item/JLT_2008_18_3_JLT_2008_18_3_a13/