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8.26 (1982)

Solved

We call a variety passable if there exists an unrefinable chain of its subvarieties which is well-ordered by inclusion. For example, every variety generated by its finite groups is passable – this is an easy consequence of (H. Neumann, Varieties of groups, Berlin et al., Springer, 1967, Chapter 5). Do there exist non-passable varieties of groups?

Contributor: A. V. Kuznetsov

Progress

Yes, there do (M. I. Anokhin, Moscow Univ. Math. Bull., 51, no. 1 (1996), 48–49).

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