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Journal of Lie Theory 28 (2018), No. 2, 427--442
Copyright Heldermann Verlag 2018

On Complemented Non-Abelian Chief Factors of a Lie Algebra

Zekiye Ciloglu
Dept. of Mathematics, Suleyman Demirel University, Isparta 32260, Turkey

David A. Towers
Dept. of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, England

The number of Frattini chief factors or of chief factors which are complemented by a maximal subalgebra of a finite-dimensional Lie algebra $L$ is the same in every chief series for L, by Theorem 2.3 of D. A. Towers [Maximal subalgebras and chief factors of Lie algebras, J. Pure Appl. Algebra 220 (2016) 482--493]. However, this is not the case for the number of chief factors which are simply complemented in L. In this paper we determine the possible variation in that number. The same question for groups has been considered by Seral and Lafuente [On complemented nonabelian chief factors of a finite group, Israel J. Math. 106 (1998) 177--188].

Keywords: L-Algebras, L-Equivalence, c-factor, m-factor, cc'-type.

MSC: 17B05, 17B20, 17B30, 17B50

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