Relations between Simplicial Groups, 3-Crossed Modules and 2-Quadratic Modules

In this paper, we define two-quadratic module and explore the relations among two-quadratic modules, three-crossed modules and simplicial groups.

Category X(R) and A-groups

New groups: X-groups are constructed. These groups are easy to calculateand they reflect more general properties of rings than K0-groups. As their applications, some characteristics of group rings with torsion-free K0-groups are obtained.