Minimal left ideals of the superextensions of groups

In the talk we shall discuss the structure of minimal (left) ideals of the superextensions of Abelian groups G. We define a group G to be odd if the order of each element x of G is odd. We prove that a group G is odd if and only if all the minimal left ideals of the semigroup of maximal linked systems are singletons. In this case the minimal ideal of the superextensions of G is a closed right zeros semigroup consisting of invariant maximal linked systems.