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Modular group
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===Braid group=== [[File:Braid-modular-group-cover.svg|thumb|376px|The [[braid group]] {{math|''B''<sub>3</sub>}} is the [[universal central extension]] of the modular group.]] The [[braid group]] {{math|''B''<sub>3</sub>}} is the universal central extension of the modular group, with these sitting as lattices inside the (topological) universal covering group {{math|{{overline|SL<sub>2</sub>('''R''')}} β PSL<sub>2</sub>('''R''')}}. Further, the modular group has a trivial center, and thus the modular group is isomorphic to the [[quotient group]] of {{math|''B''<sub>3</sub>}} modulo its [[center (group theory)|center]]; equivalently, to the group of [[inner automorphism]]s of {{math|''B''<sub>3</sub>}}. The braid group {{math|''B''<sub>3</sub>}} in turn is isomorphic to the [[knot group]] of the [[trefoil knot]].
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