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PGL2

PGL2

Topics referred to by the same term

PGL2 may refer to SDHAF2, a gene on chromosome 11 in humans for the group P G L 2 {\displaystyle \mathrm {PGL} _{2}} in mathematics, see projective linear

PGL2

Real projective line

Projective line over the real numbers

quotient group PGL2(R) = GL2(R)/R×. By the above, there is an induced faithful action of PGL2(R) on P1(R). For this reason, the group PGL2(R) may also be

Real projective line

Real_projective_line

Heawood graph

Undirected graph with 14 vertices

group of the Heawood graph is isomorphic to the projective linear group PGL2(7), a group of order 336. It acts transitively on the vertices, on the edges

Heawood graph

Heawood_graph

Projective line

Line with a point at infinity added

transitive, so that P1(K) is a homogeneous space for the group, often written PGL2(K) to emphasise the projective nature of these transformations. Transitivity

Projective line

Projective_line

Hurwitz's automorphisms theorem

Theorem in algebraic geometry

over the prime field has genus g = (p − 1)/2 but is acted on by the group PGL2(p) of order p3 − p. One of the fundamental themes in differential geometry

Hurwitz's automorphisms theorem

Hurwitz's_automorphisms_theorem

Exceptional isomorphism

Mathematical coincidence

dihedral group of order 6, A4 ≅ PSL2(3), S4 ≅ PGL2(3) ≅ PSL2(Z / 4), A5 ≅ PSL2(4) ≅ PSL2(5), S5 ≅ PΓL2(4) ≅ PGL2(5), A6 ≅ PSL2(9) ≅ Sp4(2)′, S6 ≅ Sp4(2), A8

Exceptional isomorphism

Exceptional_isomorphism

Pheochromocytoma

Tumor of the adrenal medulla which secretes adrenal hormones

and neck paraganglioma, pheochromocytoma, gastrointestinal stromal tumor PGL2 SDHAF2 100% Low Head and neck paraganglioma PGL3 SDHC Autosomal Dominant

Pheochromocytoma

Janko group J2

Sporadic simple group

centralizer has structure 4.S4, which contains 6 additional involutions. 2 3.PGL2(9) 2,160 = 24·33·5 280 = 23·5·7 normalizer of a subgroup of order 3 (class

Janko group J2

Janko_group_J2

Coxeter graph

Cubic graph with 28 vertices and 42 edges

Coxeter Vertices 28 Edges 42 Radius 4 Diameter 4 Girth 7 Automorphisms 336 (PGL2(7)) Chromatic number 3 Chromatic index 3 Book thickness 3 Queue number 2

Coxeter graph

Coxeter_graph

Rigid analytic space

Analogue of a complex analytic space over a nonarchimedean field

compactification of the inductive limit of affine Bruhat–Tits buildings for PGL2(F), as F varies over finite extensions of Qp, when the buildings are given

Rigid analytic space

Rigid_analytic_space

Klein graphs

Two special graphs in graph theory

28-vertex Coxeter graph. The automorphism group of the Klein graph is the group PGL2(7) of order 336, which has PSL2(7) as a normal subgroup. This group acts

Klein graphs

Klein_graphs

Hereditary cancer syndrome

Inherited genetic condition that predisposes a person to cancer

paraganglioma have affected fathers rather than affected mothers. PGL1 and PGL2 are autosomal dominant with imprinting. PGL-4 is associated with SDHB mutation

Hereditary cancer syndrome

Hereditary_cancer_syndrome

Plastoglobulin

Maryland conducted research whereby they inactivated the genes (pgl1 and pgl2) encoding for plastoglobulin-like proteins in Synechocystis. The results

Plastoglobulin

Automorphisms of the symmetric and alternating groups

Aspect of mathematical group theory

the k-automorphism group of X, which is the semi-direct product G of PGL2(K) = PGL2(9) against the Galois involution. This map carries the simple group

Automorphisms of the symmetric and alternating groups

Automorphisms_of_the_symmetric_and_alternating_groups

110-vertex Iofinova–Ivanov graph

Semi-symmetric cubic graph with 110 vertices and 165 edges

symmetry group of the 110-vertex Iofina-Ivanov is the projective linear group PGL2(11), with 1320 elements. Few graphs show semi-symmetry: most edge-transitive

110-vertex Iofinova–Ivanov graph

110-vertex_Iofinova–Ivanov_graph

Zassenhaus group

line. It has order (q + 1)q(q − 1)/2. The projective general linear group PGL2(Fq) for q > 3. It has order (q + 1)q(q − 1). A certain group containing PSL2(Fq)

Zassenhaus group

Zassenhaus_group

SDHAF2

Protein-coding gene in humans

HA, Jansen JC, Kremer H, Bayley JP, Cremers CW (January 2011). "SDHAF2 (PGL2-SDH5) and hereditary head and neck paraganglioma". Clinical Cancer Research

SDHAF2