Journal of Lie Theory

no. 2
On Complemented Non-Abelian Chief Factors of a Lie Algebra
Zekiye Ciloglu1; David A. Towers2
1Dept. of Mathematics, Suleyman Demirel University, Isparta 32260, Turkey
2Dept. of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, England
Journal of Lie Theory, Volume 28 (2018) no. 2, pp. 427-442
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].
DOI: 10.5802/jolt.1008
Classification: 17B05, 17B20, 17B30, 17B50
Keywords: L-Algebras, L-Equivalence, c-factor, m-factor, cc'-type

Zekiye Ciloglu  1 ; David A. Towers  2

1 Dept. of Mathematics, Suleyman Demirel University, Isparta 32260, Turkey
2 Dept. of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, England 
Zekiye Ciloglu; David A. Towers. On Complemented Non-Abelian Chief Factors of a Lie Algebra. Journal of Lie Theory, Volume 28 (2018) no. 2, pp. 427-442. doi: 10.5802/jolt.1008
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     title = {On {Complemented} {Non-Abelian} {Chief} {Factors} of a {Lie} {Algebra}},
     journal = {Journal of Lie Theory},
     pages = {427--442},
     year = {2018},
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     doi = {10.5802/jolt.1008},
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