Norm formulas for finite groups and induction from elementary abelian subgroups
نویسندگان
چکیده
It is known that the norm map NG 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 NE for E is surjective. Equivalently, there exists an element xG ∈ R with NG(xG) = 1 if and only for every elementary abelian subgroup E there exists an element xE ∈ R such that NE(xE) = 1. When the ring R is noncommutative, it is an open problem to find an explicit formula for xG in terms of the elements xE. 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. Mathematics Subject Classification (2000): 16W22, 16U99, 20C10, 20D15, 20J05
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