Submission date: 9 February 2010.

Abstract:

We prove for Chevalley groups over infinite fields, connected perfect linear algebraic groups, infinite permutation and infinite dimensional general linear groups, a model theoretical phenomenon called absolute connectedness. Namely, G is absolutely connected if for an arbitrary first order structure on G, working in a saturated extension, G does not have any proper definable, type definable or invariant under automorphisms subgroup of bounded index i.e. G=G^{0}=G^{00}=G^{oo}.

Mathematics Subject Classification: Primary 03C60, 20G15; Secondary 20E45, 03C98.

Keywords and phrases: Chevalley groups, prefect linear algebraic groups

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