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8.20 (1982)

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What is the cardinality of the set of all varieties covering an abelian (nilpotent? Cross? hereditarily finitely based?) variety of groups? The question is related to 4.46 and 4.73.

Contributor: Yu. G. Kleiman

Progress

There are continually many varieties covering the variety $\mathfrak{A}$ of abelian groups, as well as the variety $\mathfrak{A}_n$ of abelian groups of sufficiently large odd exponent $n$ (P. A. Kozhevnikov, On varieties of groups of large odd exponent, Dep. 1612-V00, VINITI, Moscow, 2000 (Russian); S. V. Ivanov, A. M. Storozhev, Contemp. Math., 360 (2004), 55–62).

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