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8.19 (1982)

Open

Which of the following properties of (soluble) varieties of groups are equivalent to one another:
$\qquad$ 1) to satisfy the minimum condition for subvarieties;
$\qquad$ 2) to have at most countably many subvarieties;
$\qquad$ 3) to have no infinite independent system of identities?

Contributor: Yu. G. Kleiman

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