Ein Satz über die Werte von quadratischen Formen über Körper.
We give necessary and sufficient conditions for an orthogonal group defined over a global field of characteristic to contain a maximal torus of a given type.
We present a survey of results on word equations in simple groups, as well as their analogues and generalizations, which were obtained over the past decade using various methods: group-theoretic and coming from algebraic and arithmetic geometry, number theory, dynamical systems and computer algebra. Our focus is on interrelations of these machineries which led to numerous spectacular achievements, including solutions of several long-standing problems.