Projective Representations of Abelian Groups

Let be a factor system for the locally compact abelian group G. Then we show that the finite-dimensional unitary irreducible projective representations of G, having factor system , possess a common dimension <!-- MATH $d(\omega )$ --> . Using a characterisation of <!-- MATH $d(\omega )$ --> as the index in G of a maximal subgroup on which is symmetric we derive a formula for <!-- MATH $d(\omega )$ --> in the case that G is discrete and finitely generated.