Exıstentıally kapalı gruplar

A group G is called an Existentially Closed Group (Algebraically Closed Group) if for every finite system of equations and inequations with coefficients from G which has a solution in an over group H \geq G, has a solution in G. Existentially closed groups were introduced by W. R. Scott in 1951. The notion of existentially closed groups is close to the notion of algebraically closed fields but there are substantial differences. Existentially closed groups were studied and advanced by B. H. Neumann. In this survey thesis we have studied the articles of B. H. Neumann and the paper of W. R. Scott.