High Quality Content by WIKIPEDIA articles! In mathematics, strong approximation in linear algebraic groups is an important arithmetic property of matrix groups. In rough terms, it explains to what extent there can be an extension of the Chinese remainder theorem to various kinds of matrices. For example, for orthogonal matrices, there cannot be such an extension and there is a theory explaining why there is, and where the problem lies (it is in the spin groups). Strong approximation was established in the 1960s and 1970s, for algebraic groups that are semisimple groups and simply-connected, for global fields. The results for number fields are due to Martin Kneser and Vladimir Platonov; the function field case, over finite fields, is due to Grigory Margulis and Gopal Prasad. In the number field case a result over local fields, the Kneser-Tits conjecture of Kneser and Jacques Tits, was proved along the way.

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