Abstract

Assume$G\prec H$are groups and${\cal A}\subseteq {\cal P}(G),\ {\cal B}\subseteq {\cal P}(H)$are algebras of sets closed under left group translation. Under some additional assumptions we find algebraic connections between the Ellis [semi]groups of theG-flow$S({\cal A})$and theH-flow$S({\cal B})$. We apply these results in the model theoretic context. Namely, assumeGis a group definable in a modelMand$M\prec ^* N$. Using weak heirs and weak coheirs we point out some algebraic connections between the Ellis semigroups$S_{ext,G}(M)$and$S_{ext,G}(N)$. Assuming every minimal left ideal in$S_{ext,G}(N)$is a group we prove that the Ellis groups of$S_{ext,G}(M)$are isomorphic to closed subgroups of the Ellis groups of$S_{ext,G}(N)$.