Abstract
If V is a variety of metabelian Lie algebras then V has a finite basis for its laws [3]. The proof of this result is similar to Cohen's proof that varieties of metabelian groups have the finite basis property [1]. However there are centre-by-metabelian Lie algebras of characteristic 2 which do not have a finite basis for their laws [4] this contrasts with McKay's recent result that varieties of centre-by-metabelian groups do have the finite basis property [2]. The rollowing theorem shows that once again “2” is the odd man out.
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