On the surjectivity of some trace maps
LetK be a commutative ring with a unit element 1. Let Γ be a finite group acting onK via a mapt: Γ→Aut(K). For every subgroupH≤Γ define tr H :K→K H by tr h (x)=Σσ∈H σ(x). We proveTheorem: trΓ is surjective onto K Γ if and only if tr P is surjective onto K P for every (cyclic) prime order subgroup P of Γ.
This is false for certain non-commutative ringsK.
KeywordsFinite Group Commutative Ring Prime Order Noetherian Ring Projective Resolution
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