  It is known that the norm map N_G for a finite group G acting on a ring R is
surjective if and only if for every elementary abelian subgroup E of G the norm
map N_E for E is surjective. Equivalently, there exists an element x_G in R
with N_G(x_G) = 1 if and only for every elementary abelian subgroup E there
exists an element x_E in R such that N_E(x_E) = 1. When the ring R is
noncommutative, it is an open problem to find an explicit formula for x_G in
terms of the elements x_E. In this paper we present a method to solve this
problem for an arbitrary group G and an arbitrary group action on a ring.Using
this method, we obtain a complete solution of the problem for the quaternion
and the dihedral 2-groups,and for a group of order 27. We also show how to
reduce the problem to the class of (almost) extraspecial p-groups.
