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We represent quantum observables as POVMs (normalized positive operatorvalued measures) and consider convex sets of observables which are covariantwith respect to a unitary representation of a locally compact Abelian symmetrygroup $G$. The value space of such observables is a transitive $G$-space. Wecharacterize the extreme points of covariant observables and also determine thecovariant extreme points of the larger set of all quantum observables. Theresults are applied to position, position difference and time observables.

Extreme Covariant Quantum Observables in the Case of an Abelian Symmetry Group and a Transitive Value Space