Abstract:An algebraic structure is said to be congruence permutable if its arbitrary congruences $\alpha$ and $\beta$ satisfy the equation $\alpha \circ \beta =\beta \circ \alpha$, where $\circ$ denotes the usual composition of binary relations. To an arbitrary $G$-set $X$ satisfying $G\cap X=\emptyset$, we assign a semigroup $(G,X,0)$ on the base set $G\cup X\cup \{ 0\}$ containing a zero element $0\notin G\cup X$, and examine the connection between the congruence permutability of the $G$-set $X$ and the semigroup $(G,X,0)$.
Keywords: $G$-set; congruence permutable algebras; semigroup
DOI: DOI 10.14712/1213-7243.2020.019
AMS Subject Classification: 20E15 20M05