Groups graded by finite root systems (Q1802566)

Let \(\text{St}(\Delta,R)\) be the Steinberg group defined by the data of a ring \(R\) and a root system \(\Delta\). The author studies the relationship between the group-theoretic structure of \(\text{St}(\Delta,R)\) and the associated ring \(R\). He introduces graded groups which are groups satisfying some axioms that are basic properties of \(\text{St}(\Delta,R)\), and then shows that these properties suffice to determine the structure of graded groups, by constructing a ring out of a graded group. Also the central extensions of graded groups are studied.