Abstract
A Steinberg group St(Δ, R) is defined by the data of a ring R and a root system Δ. This paper aims to study the relationship between the group-theoretic structure of a Steinberg group and the associated ring. We introduce graded groups which are groups satisfying some axioms that are basic properties of St(Δ, R) , and then show that these properties suffice to determine the structures of graded groups, by constructing a ring out of a graded group. Also the central extensions of graded groups are studied.
