THE NONABELIAN TENSOR SQUARE AND SCHUR MULTIPLICATOR OF NILPOTENT GROUPS OF CLASS-2

The nonabelian tensor square and the Schur multiplicator are determine d for arbitrary groups of class 2 in a closed form. A functorial descr iption is given in terms of a polynomial quotient of the integral grou p 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 pol ynomial maps and constructions in the sense of Passi. (C) 1996 Academi c Press, Inc.