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On $ n$-maximal subalgebras of Lie algebras


Author: David A. Towers
Journal: Proc. Amer. Math. Soc. 144 (2016), 1457-1466
MSC (2010): Primary 17B05, 17B30, 17B50
DOI: https://doi.org/10.1090/proc/12821
Published electronically: August 12, 2015
MathSciNet review: 3451224
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Abstract: A $ 2$-maximal subalgebra of a Lie algebra $ L$ is a maximal subalgebra of a maximal subalgebra of $ L$. Similarly we can define $ 3$-maximal subalgebras, and so on. There are many interesting results concerning the question of what certain intrinsic properties of the maximal subalgebras of a Lie algebra $ L$ imply about the structure of $ L$ itself. Here we consider whether similar results can be obtained by imposing conditions on the $ n$-maximal subalgebras of $ L$, where $ n>1$.


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Additional Information

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

DOI: https://doi.org/10.1090/proc/12821
Keywords: Lie algebras, maximal subalgebra, $n$-maximal, Frattini ideal, solvable, supersolvable, nilpotent
Received by editor(s): February 13, 2015
Received by editor(s) in revised form: April 20, 2015
Published electronically: August 12, 2015
Communicated by: Kailash C. Misra
Article copyright: © Copyright 2015 American Mathematical Society

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