Explicit elements of norm one for cyclic groups

Eli Aljadeff (1) , Christian Kassel (2)

1 TECHNION - Department of Mathematics
2 IRMA - Institut de Recherche Mathématique Avancée

Let G be a cyclic p-group of order p^n acting by automorphisms on a (non-necessarily commutative) ring R. Suppose there is an element x in R such that (1 + t + ... + t^{p-1})(x) = 1, where t is an element of order p in G. We show how to construct an element y in R such that (1 + s + ... + s^{p^n-1})(y) = 1, where s is a generator of G.

Mots clés: ring; group action; cyclic group; homology

Domaines: Anneaux et algèbres [math.RA]

Eli Aljadeff, Christian Kassel. Explicit elements of norm one for cyclic groups. 2000. ⟨hal-00124698⟩