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Subalgebras that cover or avoid chief factors of Lie algebras


Author: David A. Towers
Journal: Proc. Amer. Math. Soc. 143 (2015), 3377-3385
MSC (2010): Primary 17B05, 17B30, 17B50
DOI: https://doi.org/10.1090/S0002-9939-2015-12533-6
Published electronically: March 18, 2015
MathSciNet review: 3348780
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Abstract: We call a subalgebra $ U$ of a Lie algebra $ L$ a $ CAP$-subalgebra of $ L$ if for any chief factor $ H/K$ of $ L$, we have $ H \cap U = K \cap U$ or $ H+U = K+U$. In this paper we investigate some properties of such subalgebras and obtain some characterizations for a finite-dimensional Lie algebra $ L$ to be solvable under the assumption that some of its maximal subalgebras or $ 2$-maximal subalgebras be $ CAP$-subalgebras.


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Additional Information

David A. Towers
Affiliation: Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, England
Email: d.towers@lancaster.ac.uk

DOI: https://doi.org/10.1090/S0002-9939-2015-12533-6
Keywords: Lie algebras, solvable, chief factor, cover, avoid
Received by editor(s): January 31, 2014
Received by editor(s) in revised form: April 1, 2014
Published electronically: March 18, 2015
Communicated by: Kailash Misra
Article copyright: © Copyright 2015 American Mathematical Society