10.2 (1986)

A mixed identity of a group $G$ is, by definition, an identity of an algebraic system obtained from $G$ by supplementing its signature by some set of 0-ary operations. One can develop a theory of mixed varieties of groups on the basis of this notion (see, for example, V. S. Anashin, Math. USSR Sbornik, 57 (1987), 171–182).

Construct an example of a class of groups which is not a mixed variety, but which is closed under taking factor-groups, Cartesian products, and those subgroups of Cartesian powers that contain the diagonal subgroup.