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A subalgebra B of a Lie algebra L is called a c-ideal of L if there is an ideal C of L such that L = B + C and B \cap C \leq B_L, where B_L is the largest ideal of L contained in B. This is analogous to the concept of c-normal subgroup, which has been studied by a number of authors. We obtain some properties of c-ideals and use them to give some characterisations of solvable and supersolvable Lie algebras. We also classify those Lie algebras in which every one-dimensional subalgebra is a c-ideal

Year: 2009

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- (2005). A note on c-normal subgroups of ﬁnite groups.
- (1973). A.: A Frattini theory for algebras.
- (1972). Abstract Lie algebras.
- (1996). C-normality of groups and its properties.
- (1962). Nilpotency of Lie algebras.
- (1981). On Lie algebras in which modular pairs of subalgebras are permutable.
- (1984). On subalgebras of simple Lie algebras of characteristic p
- (1967). On the cohomology of soluble Lie algebras.
- (2000). Some conditions for solubility.
- (1956). Sous-alg` ebres de Cartan et d´ ecompositions de Levi dans les alg` ebres de Lie (French).
- (2000). The inﬂuence of c-normality on the structure of ﬁnite groups.
- (1998). The inﬂuence of minimal subgroups on the structure of ﬁnite groups,
- (2000). The inﬂuence of minimal subgroups on the structure of ﬁnite groups.

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