Abstract
If k is a subfield of Q(em) then the cohomology group H2(k (en)/k) is isomorphic to H(k(en′ )/k) with gcd(m, n ′) = 1. This enables us to reduce a cyclotomic k-algebra over k(en) to the one over k(en′ ). A radical extension in projective Schur algebra theory is regarded as an analog of cyclotomic extension in Schur algebra theory. We will study a reduction of cohomology group of radical extension and show that a Galois cohomology group of a radical extension is isomorphic to that of a certain subextension of radical extension. We then draw a cohomological characterization of radical group.
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