Abstract

We shall consider }~l'tsev classes possessing the CPR-property, i.e., classes in which all varieties are congruence-permutable and congruence-regular. An infinite independent set of strong Mal'tsev conditions implying the CPR-property will be constructed, and an 2@/ class exhibited which has this property and is not an S~@ -class. This answers a question of Baldwin and Barman [1] about the distinction between properties SG~ and S?~ . I t ~ii be recalled that Baldwin and Barman [i] constructed an example of an ~6 -class which is not $6~ We shall also construct 2 ~ ~-classes in which every variety has the (~W)-property, i.e., has only finitely many nonisomorphic free algebras of finite rank.

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