Complements of Intervals and Prefrattini Subalgebras of Solvable Lie Algebras

Details Complements of Intervals and Prefrattini Subalgebras of Solvable Lie Algebras Complements of Intervals and Prefrattini Subalgebras of Solvable Lie Algebras

2011-04-19

arxiv.org/abs/1104.3774v1

Mathematics

Rings and Algebras

Scientific paper

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.

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