Structure of groups of rational points of classical algebraic groups over number fields (Q921120)

The present paper discusses the structure of groups of rational points of classical algebraic groups over an algebraic number field K. The authors prove that, if G is a simple, simply connected algebraic group over K, which is of one of the following types: \(B_{\ell}\) (\(\ell \geq 2)\), \(C_{\ell}\) (\(\ell \geq 2)\), \(D_{\ell}\) (\(\ell \geq 4\), except \({}^ 3D_ 4\) and \({}^ 6D_ 4)\), or the special unitary group \(SU_ m(L| K,f)\) of type \({}^ 2A_{m-1}\) (m\(\geq 3)\), of a non-degenerate m-dimensional Hermitian form f over a quadratic extension \(L| K\), then \(G_ K\) is projectively simple. The authors also prove that, if G is a simple K-defined group of type \(G_ 2\), then \(G_ k\) does not have proper non-central normal subgroups, i.e., \(G_ K\) is projectively simple.