Complements of intervals and prefrattini subalgebras of solvable Lie algebras

Towers, David

doi:10.1090/S0002-9939-2012-11521-7

Complements of intervals and prefrattini subalgebras of solvable Lie algebras
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Proc. Amer. Math. Soc. 141 (2013), 1893-1901 Request permission

Abstract:

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. Kurzweil for groups by first considering complements in subalgebra intervals. Conjugacy of these subalgebras is established for a large class of solvable Lie algebras.

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