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- Circle_group abstract "In mathematics, the circle group, denoted by T, is the multiplicative group of all complex numbers with absolute value 1, i.e., the unit circle in the complex plane.The circle group forms a subgroup of C×, the multiplicative group of all nonzero complex numbers. Since C× is abelian, it follows that T is as well. The circle group is also the group U(1) of 1×1 unitary matrices; these act on the complex plane by rotation about the origin. The circle group can be parametrized by the angle θ of rotation byThis is the exponential map for the circle group.The circle group plays a central role in Pontryagin duality, and in the theory of Lie groups.The notation T for the circle group stems from the fact that Tn (the direct product of T with itself n times) is geometrically an n-torus. The circle group is then a 1-torus.".
- Circle_group thumbnail Circle-group.svg?width=300.
- Circle_group wikiPageExternalLink watch?v=-ypicun4AbM&list=PL0F555888A4C2329B.
- Circle_group wikiPageID "508177".
- Circle_group wikiPageRevisionID "605429416".
- Circle_group hasPhotoCollection Circle_group.
- Circle_group subject Category:Group_theory.
- Circle_group subject Category:Lie_groups.
- Circle_group subject Category:Topological_groups.
- Circle_group type Abstraction100002137.
- Circle_group type Group100031264.
- Circle_group type LieGroups.
- Circle_group type TopologicalGroups.
- Circle_group comment "In mathematics, the circle group, denoted by T, is the multiplicative group of all complex numbers with absolute value 1, i.e., the unit circle in the complex plane.The circle group forms a subgroup of C×, the multiplicative group of all nonzero complex numbers. Since C× is abelian, it follows that T is as well. The circle group is also the group U(1) of 1×1 unitary matrices; these act on the complex plane by rotation about the origin.".
- Circle_group label "Cercle unité".
- Circle_group label "Circle group".
- Circle_group label "Cirkelgroep".
- Circle_group label "Grupa kołowa".
- Circle_group label "Grupo circular".
- Circle_group label "Gruppo circolare".
- Circle_group label "Kreisgruppe".
- Circle_group label "U(1)".
- Circle_group label "زمرة الدائرة".
- Circle_group label "圓群".
- Circle_group sameAs Kreisgruppe.
- Circle_group sameAs Grupo_circular.
- Circle_group sameAs Cercle_unité.
- Circle_group sameAs Gruppo_circolare.
- Circle_group sameAs Cirkelgroep.
- Circle_group sameAs Grupa_kołowa.
- Circle_group sameAs m.02jrlh.
- Circle_group sameAs Q2608380.
- Circle_group sameAs Q2608380.
- Circle_group sameAs Circle_group.
- Circle_group wasDerivedFrom Circle_group?oldid=605429416.
- Circle_group depiction Circle-group.svg.
- Circle_group isPrimaryTopicOf Circle_group.