Goudarzi, L. (2018). On permutably complemented subalgebras of finite dimensional Lie algebras. Algebraic Structures and Their Applications, 5(2), 15-21.

Leila Goudarzi. "On permutably complemented subalgebras of finite dimensional Lie algebras". Algebraic Structures and Their Applications, 5, 2, 2018, 15-21.

Goudarzi, L. (2018). 'On permutably complemented subalgebras of finite dimensional Lie algebras', Algebraic Structures and Their Applications, 5(2), pp. 15-21.

Goudarzi, L. On permutably complemented subalgebras of finite dimensional Lie algebras. Algebraic Structures and Their Applications, 2018; 5(2): 15-21.

On permutably complemented subalgebras of finite dimensional Lie algebras

^{}Department of mathematics, University of Ayatollah Alozma Boroujerdi, Boroujerd, Iran

Abstract

Let $L$ be a finite-dimensional Lie algebra. We say a subalgebra $H$ of $L$ is permutably complemented in $L$ if there is a subalgebra $K$ of $L$ such that $L=H+K$ and $H\cap K=0$. Also, if every subalgebra of $L$ is permutably complemented in $L$, then $L$ is called completely factorisable. In this article, we consider the influence of these concepts on the structure of a Lie algebra, in particular, we obtain some characterizations for supersolvability of a finite-dimensional Lie algebra in terms of permutably complemented subalgebras.

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