Groups of automorphisms and chains of closed subgroups (Q699100)

The author studies the subgroup structure of automorphism groups of models. The main result is as follows: Theorem. Let \(M\) be a model of regular cardinality \(\lambda\). If \(\lambda>\omega\) then we assume \(M\) to be homogeneous. Suppose that \(2^\mu<2^\lambda\) for every \(\mu<\lambda\). Then the group Aut\((M)\) is not a union of a \(\lambda\)-chain of closed non-open proper subgroups.