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 $n=2,2.5,3$.
@article{118958, author = {Boris M. Vernikov}, title = {On congruences of $G$-sets}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {38}, year = {1997}, pages = {603-613}, zbl = {0938.08002}, mrnumber = {1485081}, language = {en}, url = {http://dml.mathdoc.fr/item/118958} }
Vernikov, Boris M. On congruences of $G$-sets. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) pp. 603-613. http://gdmltest.u-ga.fr/item/118958/
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