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Projective characters of degree one and the inflation-restriction sequence

1989
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Journal of the Australian Mathematical Society
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Let G be a finite group, a be a fixed cocycle of G and Proj(G, a) denote the set of irreducible projective characters of G lying over the cocycle a. Suppose N is a normal subgroup of G. Then the author shows that there exists a Ginvariant element of Proj(JV, apt) of degree 1 if and only if [a] is an element of the image of the inflation homomorphism from M(G/N) into M(G), where M(G) denotes the Schur multiplier of G. However in many situations one can produce such G-invariant characters where

doi:10.1017/s1446788700030731
fatcat:xxjteegvn5cxbd7f23o7aamzge