A group $G$ is existentially closed (algebraically closed) if every finite system of equations and in-equations that has coefficients in $G$ and has a solution in an overgroup $H\geq G$ has a solution in $G$. Existentially closed groups were introduced by W. R. https://www.roneverhart.com/5-15P-ANGLE-PLUG-B-W-HUBBELL-HBL5266CA/