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Lie algebras all of whose subalgebras are supersolvable. (English) Zbl 0587.17006

Lie algebras and related topics, Proc. Semin., Windsor/Ont. 1984, CMS Conf. Proc. 5, 209-218 (1986).
[For the entire collection see Zbl 0574.00001.]
The authors investigate certain classes of solvable Lie algebras which are minimal non-supersolvable. They obtain the basic structure theorem for such algebras if either the derived algebra is nilpotent or the Frattini ideal is trivial. They then investigate the nil-radical for these algebras. Finally some results on elementary Lie algebras which extend results of D. A. Towers [J. Lond. Math. Soc., II. Ser. 7, 295-302 (1973; Zbl 0267.17006)] are included.
Reviewer: E.L.Stitzinger

MSC:

17B30 Solvable, nilpotent (super)algebras
17B05 Structure theory for Lie algebras and superalgebras