Reduced crossed products over discrete groups are prime, and the ideal intersection property holds for FC-hypercentral groups, exactly when certain conjugacy classes of elements acting 'inner' on invariant subalgebras are infinite.
Blackadar,Operator algebras: Theory of C*-algebras and von Neumann algebras, Encyclopaedia Math
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Primality and the ideal intersection property for reduced crossed products
Reduced crossed products over discrete groups are prime, and the ideal intersection property holds for FC-hypercentral groups, exactly when certain conjugacy classes of elements acting 'inner' on invariant subalgebras are infinite.