@article { author = {Goudarzi, Leila}, title = {On permutably complemented subalgebras of finite dimensional Lie algebras}, journal = {Algebraic Structures and Their Applications}, volume = {5}, number = {2}, pages = {15-21}, year = {2018}, publisher = {Yazd University}, issn = {2382-9761}, eissn = {2423-3447}, doi = {10.22034/as.2018.1215}, 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.}, keywords = {Lie algebra,permutably complemented,completely factorisable,solvable,supersolvable}, url = {https://as.yazd.ac.ir/article_1215.html}, eprint = {https://as.yazd.ac.ir/article_1215_addd86682e26e2e4e9874fe0d2069411.pdf} }