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We consider varieties V = A A A with m prime to p . We P ŝ how that the subvariety lattice of V. is distributive and has descending chain condition and that A A is its only just "FT non-Cross subvariety. When m is prime we determine the join-irreducible subvarieties of V. . The method involves fairly detailed description of the structure of non-nilpotent critical groups in V_ . Even before these examples of Ol'shanskii and Vaughan-Lee were known the range of questions considered, for locallydoi:10.1017/s0004972700045901 fatcat:wvwicaoxuber7dubszhyokxd3e