Groups with faithful irreducible projective unitary representations
Résumé
For a countable group $\Gamma$ and a multiplier $\zeta \ Z^2(\Gamma,T)$, we study the property of $\Gamma$ having a unitary projective -representation which is both irreducible and projectively faithful. Theorem 1 shows that this property is equivalent to $\Gamma$ being the quotient of an appropriate group by its centre. Theorem 4 gives a criterion in terms of the minisocle of $\Gamma$. Several examples are described to show the existence of various behaviours.
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