# An application of model theory to real andp-adic algebraic groups

- Authors
- Journal
- Journal of Algebra 0021-8693
- Publisher
- Elsevier
- Publication Date
- Volume
- 126
- Issue
- 1
- Identifiers
- DOI: 10.1016/0021-8693(89)90323-2
- Disciplines

## Abstract

Abstract We use quantifier elimination for R and Q p to give elementary proofs of some basic results on algebraic groups G over these fields. In particular (i) the commutator subgroup is closed (and in the real case, semialgebraic), and (ii) if G is simple then any homomorphism of G into a compact topological group is continuous ( van de Waerden, Math. Z. 36 (1933) , 780–786; A. Borel and J. Tits, Ann. of Math. (2) 97 (1973) , 499–571).

## There are no comments yet on this publication. Be the first to share your thoughts.