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SCAP-subalgebras of Lie algebras

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Abstract

A subalgebra H of a finite dimensional Lie algebra L is said to be a SCAP-subalgebra if there is a chief series 0 = L 0 ⊂ L 1 ⊂... ⊂ L t = L of L such that for every i = 1, 2,..., t, we have H + L i = H + L i-1 or H ∩ L i = H ∩ L i-1. This is analogous to the concept of SCAP-subgroup, which has been studied by a number of authors. In this article, we investigate the connection between the structure of a Lie algebra and its SCAP-subalgebras and give some sufficient conditions for a Lie algebra to be solvable or supersolvable.

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Authors and Affiliations

  1. Faculty of Mathe- matical Sciences, Shahid Beheshti University, Bolvar-e-Shahid Beheshti, General Campus, P.O.Box 1983969411, Tehran, 11369, Iran

    Sara Chehrazi & Ali Reza Salemkar

Authors
  1. Sara Chehrazi
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  2. Ali Reza Salemkar
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Correspondence to Sara Chehrazi.

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Chehrazi, S., Salemkar, A.R. SCAP-subalgebras of Lie algebras. Czech Math J 66, 1177–1184 (2016). https://doi.org/10.1007/s10587-016-0317-3

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  • DOI: https://doi.org/10.1007/s10587-016-0317-3

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