## Abstract

It is known that the norm map N_{G} for the action of a finite group G on a ring R is surjective if and only if for every elementary abelian subgroup U of G the norm map N_{U} is surjective. Equivalently, there exists an element x_{G} ∈ R satisfying N_{G}(x_{G}) = 1 if and only if for every elementary abelian subgroup U there exists an element x_{U} ∈ R such that N_{U}(x_{U}) = 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_{U}. We solve this problem when the group G is abelian. The main part of the proof, which was inspired by cohomological considerations, deals with the case when G is a cyclic p-group.

Original language | English |
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Article number | BF02773156 |

Pages (from-to) | 99-108 |

Number of pages | 10 |

Journal | Israel Journal of Mathematics |

Volume | 129 |

DOIs | |

State | Published - 2002 |

Externally published | Yes |