On Complemented Non-Abelian Chief Factors of a Lie Algebra


ÇİLOĞLU ŞAHİN Z., Towers D. A.

JOURNAL OF LIE THEORY, vol.28, no.2, pp.427-442, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 28 Issue: 2
  • Publication Date: 2018
  • Journal Name: JOURNAL OF LIE THEORY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.427-442
  • Süleyman Demirel University Affiliated: Yes

Abstract

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 [4, Theorem 2.3]. 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 in [2].