Complements of Intervals and Prefrattini Subalgebras of Solvable Lie   Algebras
  In this paper we study a Lie-theoretic analogue of a generalisation of the prefrattini subgroups introduced by W. Gasch\"utz. 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. 
David A. Towers
math.RA math.GR