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PSL(2, 4) = PGL(2, 4) → S 5, of order 60, yielding the alternating group A 5. PSL(2, 5) < PGL(2, 5) → S 6, of orders 60 and 120, which yields an embedding of S 5 (respectively, A 5) as a transitive subgroup of S 6 (respectively, A 6). This is an example of an exotic map S 5 → S 6, and can be used to construct the exceptional outer ...
Since PSL(2, Z) is a subgroup of PSL(2, R), the modular group is a subgroup of the group of orientation-preserving isometries of H. [3] Tessellation of the hyperbolic ...
Theorem 11.2 shows that if 2∈π 2 then the group is PSL 2 (q), M 11, A 7, U 3 (3), or PSL 3 (3). The possibility that 2∈π 3 is ruled out by showing that any such group must be a C-group and using Suzuki's classification of C-groups to check that none of the groups found by Suzuki satisfy this condition. Thompson (1973) and Thompson (1974 ...
B or b – prefix denoting a number in billions; BA – bottom assembly (of a riser) bbl – barrel bbl/MMscf – barrels per million standard cubic feet
In mathematics, a Fuchsian group is a discrete subgroup of PSL(2,R).The group PSL(2,R) can be regarded equivalently as a group of orientation-preserving isometries of the hyperbolic plane, or conformal transformations of the unit disc, or conformal transformations of the upper half plane, so a Fuchsian group can be regarded as a group acting on any of these spaces.
Nominal Pipe Size (NPS) is a North American set of standard sizes for pipes used for high or low pressures and temperatures. [1] " Nominal" refers to pipe in non-specific terms and identifies the diameter of the hole with a non-dimensional number (for example – 2-inch nominal steel pipe" consists of many varieties of steel pipe with the only criterion being a 2.375-inch (60.3 mm) outside ...
As a topological space, PSL(2, R) can be described as the unit tangent bundle of the hyperbolic plane. It is a circle bundle, and has a natural contact structure induced by the symplectic structure on the hyperbolic plane. SL(2, R) is a 2-fold cover of PSL(2, R), and can be thought of as the bundle of spinors on the hyperbolic plane.
2 B 2 (8) The Schur multiplier has an extra Z/2Z × Z/2Z, so the Schur multiplier of the simple group has order 4 instead of 1. There is a bewildering number of "accidental" isomorphisms between various small groups of Lie type (and alternating groups). For example, the groups SL(2, 4), PSL(2, 5), and the alternating group on 5 points are all ...