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Preprint Number 2271

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2271. Adam Malinowski and Ludomir Newelski
Weak heirs, coheirs and the Ellis semigroups

Submission date: 29 September 2022


Assume G ≺ H are groups and A ⊆ P(G), B ⊆ 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 the G-flow S(A) and the H-flow S(B). We apply these results in the model theoretic context. Namely, assume G is a group definable in a model M ≺* 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).

Mathematics Subject Classification: 03C45 (Primary) 37B05 (Secondary)

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Full text arXiv 2209.14838: pdf, ps.

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