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Preprint Number 66

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66. Jakub Gismatullin and Ludomir Newelski
G-compactness and groups
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Submission date: 14 March 2007

Abstract:

Lascar described E_KP as a composition of E_L and the topological closure of E_L. We generalize this result to some other pairs of equivalence relations. Motivated by an attempt to construct a new example of a non-G-compact theory, we consider the following example. Assume G is a group definable in a structure M. We define a structure M_0 consisting of M and X as two sorts, where X is an affine copy of G and in M_0 we have the structure of M and the action of G on X. We prove that the Lascar group of M_0 is a semi-direct product of the Lascar group of M and G/GL. We discuss the relationship between G-compactness of M and M_0. This example may yield new examples of non-G-compact theories.

Mathematics Subject Classification: 03C60, 22C05, 20F28, 03H05

Keywords and phrases: strong types, G-compactness, regular action, automorphisms groups

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