Geodesic
On congruences of $G$-sets
Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) no. 3, pp. 603-613.

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We describe $G$-sets whose congruences satisfy some natural lattice or multiplicative restrictions. In particular, we determine $G$-sets with distributive, arguesian, modular, upper or lower semimodular congruence lattice as well as congruence $n$-permutable $G$-sets for $n=2,2.5,3$.
Classification : 08A30, 08A60
Keywords: $G$-set; congruence lattice; congruence distributivity; congruence modularity; congruence $n$-permutability 
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Vernikov, B. M. On congruences of $G$-sets. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) no. 3, pp. 603-613. http://geodesic.mathdoc.fr/item/CMUC_1997__38_3_a16/