Abstract :
The nonabelian tensor square and the Schur multiplicator are determined for arbitrary groups of class 2 in a closed form. A functorial description is given in terms of a polynomial quotient of the integral group ring, as well as a more explicit formula for finite groups which can be evaluated by matrix calculus. This is carried out for 2-generator groups. Also some homotopical data of the suspended classifying space of class 2 groups are derived. The approach is based on the use of polynomial maps and constructions in the sense of Passi.
