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Let K be an algebraically closed field of characteristic zero, and let K x denote the multiplicative group of K. Given a finite group G, a mapping a: GxG-» K x is called a cocycle if, for all x,y,z e 6?, a(z, ?/)a(a:y, z) = a(z, 2/z)a(y, 2) and a(*,l) = l = a (l , z). Two cocycles a, ]8 are cohomologous if there exists a mapping 8: G-> K* such that for all… (More)

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