Geodesic
Semigroup Varieties on Whose Free Objects Almost All Fully Invariant Congruences are Weakly Permutable
Algebra i logika, Tome 43 (2004) no. 6, pp. 635-649.

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A semigroup variety is said to be of index $\leqslant2$ if all nil-semigroups of the variety are semigroups with zero multiplication. We describe all semigroup varieties $\mathcal V$ of index $\leqslant2$ on free objects of which every two fully invariant congruences contained in the least semilattice congruence are weakly permutable, and semigroup varieties of index $\leqslant2$ all of whose subvarieties share the above-mentioned property.
Keywords: semigroup variety, nil-semigroup, weakly permutable congruence, fully invariant congruence. 
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B. M. Vernikov. Semigroup Varieties on Whose Free Objects Almost All Fully Invariant Congruences are Weakly Permutable. Algebra i logika, Tome 43 (2004) no. 6, pp. 635-649. http://geodesic.mathdoc.fr/item/AL_2004_43_6_a0/

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