Projective special linear group:PSL(2,R)
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Definition as a matrix group
In other words, it is defined as .
Definition as a group of fractional linear transformations
The group can be defined as the group of conformal automorphisms of the upper half-plane. In other words, it is the group of maps of the form:
where are such that these maps send the upper half-plane to itself.
|order of a group||cardinality of the continuum||Same infinite cardinality as its double cover SL(2,R).|
|exponent of a group||infinite||Same as its double cover SL(2,R).|
|composition length||1||groups with same composition length||Follows from being simple -- see projective special linear group is simple.|
|chief length||1||groups with same chief length||Follows from being simple -- see projective special linear group is simple.|
|dimension of an algebraic group||3||groups with same dimension of an algebraic group||As|
|dimension of a real Lie group||3||groups with same dimension of a real Lie group||As|