Let \(R\) be a commutative ring with identity, and let \(G\) be a Chevalley-Demazure group scheme associated with an irreducible root system. Let \(G(R)\) denote the \(R\)-valued group of \(G\), and \(E(R)\) its elementary subgroup. In the paper under review the author discusses the centers, normal subgroups and automorphisms of \(G(R)\) and \(E(R)\). For instance, the author proves that, when the rank of the root system of \(G\) is greater than 1, \(R\) is noetherian, 2 is a unit in \(R\), 3 is a unit in \(R\) if \(G\) is of type \(G_2\), and \(R\) has no quotient ring of two elements if \(G\) is of type \(B_2\) or \(G_2\), then every automorphism of \(E(R)\) or \(G(R)\) is “standard”. It covers many, but not all, earlier results on this subject.
For the entire collection see [Zbl 0824.00029].