Abstract
Various types of permutativity conditions are important in the study of (pseudo)varieties of semigroups. In previous papers of this series, minimal pseudovarieties failing certain permutativity conditions were determined. This theme is pursued here in relation to a family of conditions which appear in the investigation of power pseudovarieties of semigroups, namely, for eachk≥0, we consider the conditionC k on a semigroup that it satisfy the identityx 1 ...x k y 1 y 2 z 1 ...z n=x 1 ...x k y 2 y 1 z 1 ...z n for somen. For all minimal pseudovarieties failing Ck, a generator and finite basis of identities are specified.
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