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Let G be a finite group and let Ω be a subgroup of the multiplicative group Cˣ of complex numbers; assume that Ω contains a root ζ IGI, of unity of order IGI. I shall consider relationships between H²(G, Ω) and the Schur multiplier H²(G, Cˣ). If also Ω = Kˣ for a field K, there is a connection with the problem of writing projective representations of G in K.
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