Abstract: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 $n=2,2.5,3$.
Keywords: $G$-set, congruence lattice, congruence distributivity, congruence modularity, congruence $n$-permutability
AMS Subject Classification: 08A60, 08A30