Authors: ZEKİYE ÇİLOĞLU ŞAHİN, DAVID ANTHONY TOWERS

Abstract: A subalgebra $B$ of a Lie algebra $L$ is called a weak c-ideal of $L$ if there is a subideal $C$ 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 weakly c-normal subgroups, which has been studied by a number of authors. We obtain some properties of weak c-ideals and use them to give some characterisations of solvable and supersolvable Lie algebras. We also note that one-dimensional weak c-ideals are c-ideals.

Keywords: Weak c-ideal, Frattini ideal, Lie algebras, nilpotent, solvable, supersolvable

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