Complements of intervals and prefrattini subalgebras of solvable Lie algebras

David A. Towers
2012 Proceedings of the American Mathematical Society  
In this paper we study a Lie-theoretic analogue of a generalisation of the prefrattini subgroups introduced by W. Gaschütz. The approach follows that of P. Hauck and H. Kurtzweil for groups, by first considering complements in subalgebra intervals. Conjugacy of these subalgebras is established for a large class of solvable lie algebras.
doi:10.1090/s0002-9939-2012-11521-7 fatcat:6nuwyhkov5elxj34tuf35puoz4