Abstract
in the class whenever all n-generated subalgebras of L are in the class. Thus the classes JV of nilpotent Lie algebras and d of abelian Lie algebras are 2-recognizable. The problems are to find if a given class is n-recognizable and to find the smallest n. We consider the classes &‘JV of Lie algebras which have an abelian ideal with nilpotent quotient, JV&, of Lie algebras which have a nilpotent ideal with abelian quotient, % of supersolvable Lie algebras, and Y of solvable Lie algebras. The same notation is used for the corresponding classes of finite groups. Most notation is standard except where indicated.
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