Two Theorems on Galois Cohomology1
نویسندگان
چکیده
Notice that we have dropped the hypothesis that both k and K be Galois over the rationals. To see how Theorem 1 generalizes Yokoi's result, remember that if G has prime order p, then multiplication by p annihilates all the cohomology groups. Thus in this case the cohomology groups are determined up to isomorphism by their order. The technique used to prove Theorem 1 can be used to prove other results of a similar nature. In the same situation as above let us consider Uk, the units of K, as a Z[G] module. Then we have
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