# Hilbert's theorem 90

From Groupprops

This fact is related to: group cohomology

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## Statement

Let be a Galois extension of fields and let be the Galois group of the field extension. If is a cyclic group, then for the usual action of on , the first cohomology group is trivial. In other words:

In other words, any 1-cocycle for the action on is in fact a 1-coboundary.