Research Training Network in Model Theory
Publications > Preprint server > Preprint Number 228

Preprint Number 228

Previous Next Preprint server

228. Jakub Gismatullin
Absolute connectedness of the classical groups

Submission date: 9 February 2010.


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

Full text arXiv: pdf, ps.

Last updated: March 23 2021 10:21 Please send your corrections to: