In [3] and also in [4], Freese and McKenzie prove that a finitely generated congruence modular variety is residually small if and only if it is residually less than n for some n < ~o. In fact, they showed that i fA generates a residually small congruence modular variety and [A] = m, then "//(A) is residually less than the bound l! + m where l = m . . . . 3. They obtained this result by associat...

Using a method of R. McKenzie, we construct a finitely generated semisimple variety of infinite type, and a finitely generated nonsemisimple variety of finite type, both having arbitrarily large finite but no infinite simple members. This amplifies M. Valeriote’s negative solution to Problem 11 from [1]. R. McKenzie [2] has constructed a finitely generated variety having arbitrarily large finit...