On Congruence Permutable $G$-sets
Nagy, Attila · Repository of the Academy's Library (Library of the Hungarian Academy of Sciences) · 2018
An algebraic structure is said to be congruence permutable if its arbitrary congruences $α$ and $β$ satisfy the equation $α\circ β=β\circ α$, where $\circ$ denotes the usual composition of binary relations. For an arbitrary $G$-set $X$ with $G\cap X=\emptyset$, we define a semigroup $(G,X,0)$ with a zero $0$ ($0 otin G\cup X$), and give necessary and sufficient conditions for the congruence permutability of the $G$-set $X$ by the help of the semigroup $(G,X,0)$.