# C-Supplemented Subalgebras of Lie Algebras.

Towers, David A. (2008) C-Supplemented Subalgebras of Lie Algebras. Journal of Lie Theory, 18 (3). pp. 717-724. ISSN 0949-5932

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## Abstract

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.

Item Type: Article Journal of Lie Theory Lie algebras ; c-supplemented subalgebras ; completely factorisable algebras ; Frattini ideal ; subalgebras of codimension one. Q Science > QA Mathematics Faculty of Science and Technology > Mathematics and Statistics 860 Dr David A. Towers 19 Dec 2007 16:06 Yes Published 26 Jul 2012 18:24 http://eprints.lancs.ac.uk/id/eprint/860