C-Supplemented Subalgebras of Lie Algebras
David A. Towers

TL;DR
This paper characterizes c-supplemented Lie algebras over any field, extending the concept from group theory to Lie algebra substructures and providing a complete classification.
Contribution
It offers a comprehensive classification of c-supplemented Lie algebras, a novel extension of the subgroup concept to Lie algebra subalgebras.
Findings
Complete classification of c-supplemented Lie algebras
Extension of subgroup c-supplementation to Lie algebras
Characterization valid over any field
Abstract
A subalgebra of a Lie algebra is {\em c-supplemented} in if there is a subalgebra of with and , where is the core of in . This is analogous to the corresponding concept of a c-supplemented subgroup in a finite group. We say that is {\em c-supplemented} if every subalgebra of is c-supplemented in . We give here a complete characterisation of c-supplemented Lie algebras over a general field.
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Taxonomy
TopicsFinite Group Theory Research · Advanced Algebra and Geometry · Advanced Topics in Algebra
