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We completely determine all semigroup varieties satisfiyng a permutationalidentity of length 3 that are cancellable elements of the lattice of allsemigroup varieties. Using this result, we provide a series of new examples ofsemigroup varieties that are a modular but not cancellable elements of thislattice.

Cancellable elements of the lattice of semigroup varieties: varieties satisfying a permutational identity of length 3