Elduque, Alberto; Varea, Vicente R. 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 Cited in 1 Document MSC: 17B30 Solvable, nilpotent (super)algebras 17B05 Structure theory for Lie algebras and superalgebras Keywords:solvable Lie algebras; minimal non-supersolvable; Frattini ideal; nil- radical; elementary Lie algebras Citations:Zbl 0574.00001; Zbl 0267.17006 PDFBibTeX XML