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Journal of Algebra 303 (2006) 677706 www.elsevier.com/locate/jalgebra
 

Summary: Journal of Algebra 303 (2006) 677­706
www.elsevier.com/locate/jalgebra
Norm formulas for finite groups and induction
from elementary abelian subgroups
Eli Aljadeff a
, Christian Kassel b,
a Department of Mathematics, Technion--Israel Institute of Technology, 32000 Haifa, Israel
b Institut de Recherche Mathématique Avancée, CNRS--Université Louis Pasteur, 7 rue René Descartes,
67084 Strasbourg Cedex, France
Received 15 May 2005
Available online 15 June 2006
Communicated by Jon Carlson
Abstract
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.

  

Source: Aljadeff, Eli - Department of Mathematics, Technion, Israel Institute of Technology

 

Collections: Mathematics