{\text{For }}\gamma ={\begin{pmatrix}a&b\\c&d\end{pmatrix}}\in {\text{PSL}}(2,7){\text{ and }}x\in \mathbf {P} ^{1}\!(7),\ \gamma \cdot x={\frac {ax+b}{cx+d}}...
11 KB (1,570 words) - 08:42, 20 March 2024
characteristic −4, as a quotient of the hyperbolic plane by the symmetry group PSL(2,7) of the Fano plane. The hyperbolic area of a fundamental domain is 8π,...
146 KB (17,429 words) - 21:52, 7 September 2024
plane so as to tessellate the plane. In 1879, he examined the action of PSL(2,7), considered as an image of the modular group, and obtained an explicit...
31 KB (3,124 words) - 07:17, 20 August 2024
that no 3-dimensional figure has (rotational) symmetries equal to PSL(2,7), since PSL(2,7) does not embed as a subgroup of SO(3) (or O(3)) – it does not...
27 KB (3,263 words) - 07:08, 26 August 2024
the projective special linear group PSL(2,7) x S3 of a trio subgroup of M24 is useful for generating a basis. PSL(2,7) permutes the octads internally, in...
16 KB (2,145 words) - 15:55, 7 September 2024
second-smallest non-abelian simple group. This group is isomorphic to both PSL(2,7) and PSL(3,2). For genus 4, Bring's surface is a highly symmetric surface. For...
26 KB (3,306 words) - 11:22, 3 September 2024
projective special linear group PSL(2,7) of order 168, and every simple group of order 168 is isomorphic to PSL(2,7). The infinite alternating group...
16 KB (2,137 words) - 16:00, 22 July 2024
which commutes with a simple subgroup of order 168. A direct product PSL(2,7) × S3 in M24 permutes the octads of a trio and permutes 14 dodecad diagonal...
20 KB (2,300 words) - 10:56, 28 June 2023
in turn a subgroup of the group of isotopies described below. See also: PSL(2,7) – the automorphism group of the Fano plane. An isotopy of an algebra is...
37 KB (4,496 words) - 23:22, 28 August 2024
smallest nonabelian simple group P S L ( 2 , 7 ) . {\displaystyle \mathrm {PSL} (2,7).} From Hurwitz's automorphisms theorem, 168 is the maximum possible number...
14 KB (2,126 words) - 22:18, 16 July 2024
of Q with particular Galois groups. One curve, C168, gives Galois group PSL(2,7) from a polynomial of degree seven, and the other, C1344, gives Galois...
3 KB (504 words) - 02:12, 14 January 2021
Mathieu group M24 (section M24 from PSL(3,4))
(the symmetries of a tessellation of the genus three surface), which is PSL(2,7), which can be augmented by an additional permutation. This permutation...
26 KB (3,009 words) - 11:13, 16 May 2024
full collineation group is of order 168 and is isomorphic to the group PSL(2,7) ≈ PSL(3,2), which in this special case is also isomorphic to the general linear...
22 KB (2,841 words) - 13:36, 12 April 2024
special linear group PSL(2,7), of order 168, and the corresponding curve is the Klein quartic curve. This group is also isomorphic to PSL(3,2). Next is the...
18 KB (2,781 words) - 13:17, 26 August 2024
PSL(2,7) (order 168) and PSL(2,11) (order 660), which also admit geometric interpretations – PSL(2,5) is the symmetries of the icosahedron (genus 0), PSL(2...
48 KB (2,349 words) - 22:59, 20 April 2024
≅ PSL3(2), the second-smallest non-abelian simple group (order 168) – PSL(2,7); PSL2(9) ≅ A6; PSL4(2) ≅ A8; PSU4(2) ≅ PSp4(3), between a projective special...
7 KB (641 words) - 08:28, 20 March 2024
objects; The Eightfold Way is based on the projective special linear group PSL(2,7), a finite group of 168 elements. The sculptor Bathsheba Grossman similarly...
117 KB (12,016 words) - 13:51, 27 August 2024
A_{5}} have connections with the projective special linear groups PSL(2,5), PSL(2,7), and PSL(2,11) (orders 60, 168, and 660), which is deemed a "McKay correspondence"...
21 KB (2,595 words) - 05:49, 26 August 2024
vertices, with symmetry group the simple group of order 168, known as PSL(2,7). The resulting surface can in turn be polyhedrally immersed into Euclidean...
4 KB (423 words) - 21:54, 12 December 2023
) {\displaystyle PSL(2,11)} , following earlier constructions of a 7-fold cover with monodromy P S L ( 2 , 7 ) {\displaystyle PSL(2,7)} connected to the...
30 KB (4,171 words) - 20:41, 13 July 2024
the second smallest non-abelian simple group, which is isomorphic to PSL(2,7), and the associated Hurwitz surface (of genus 3) is the Klein quartic...
78 KB (10,928 words) - 01:40, 26 June 2024
of genus 3, with automorphism group the projective special linear group PSL(2,7), of order 84(3 − 1) = 168 = 23·3·7, which is a simple group; (or order...
5 KB (648 words) - 07:03, 8 February 2024
group of this surface is isomorphic to the projective special linear group PSL(2,7), equivalently GL(3,2) (the order 168 group of all orientation-preserving...
6 KB (695 words) - 08:13, 27 September 2023
centralizer of 3 involutions each moving 100 points A5 × D10 order 600 PGL(2,7) order 336 52:D12 order 300 A5 order 60 The maximum order of any element...
9 KB (1,022 words) - 13:58, 15 May 2024
(PSOL) with 3,7% Coronel Cláudia (PL) with 8,2% and Mateus Simões (NOVO) with 2,7% Carlos Melles (PL) with 2%, Paulo Piau (MDB) with 2%, Pastor Altamiro Alves...
88 KB (1,851 words) - 01:11, 4 September 2024
2,4 6 / 200 1979 2,8 8 / 200 2 1983 2,8 8 / 200 1987 2,7 9 / 200 1 1991 3,0 10 / 200 1 1995 2,7 7 / 200 3 1999 2,3 6 / 200 1 2003 2,2 4 / 200 2 2007 1...
11 KB (715 words) - 20:55, 3 September 2024
Datena (PSL) with 19,1% and Vinicius Poit (NOVO) with 0,7% José Luiz Datena (PSL) with 20,2% and Vinicius Poit (NOVO) with 0,7% José Luiz Datena (PSL) with...
228 KB (6,747 words) - 14:28, 15 August 2024
(PSDB) with 0,1% Eduardo Leite (PSDB) with 17% Comandante Nádia (PP) with 2,7% Eduardo Leite (PSDB) with 14,9% and Comandante Nádia (PP) with 2,5% Comandante...
100 KB (2,695 words) - 17:28, 30 May 2024
(MDB) with 3% and Marcelo Itagiba (AVANTE) with 2% Otoni de Paula (MDB) with 2,7% Cabo Daciolo (PDT) with 10% Possible electoral scenario where the presidential...
129 KB (2,869 words) - 07:53, 29 June 2024
3% – 1% – 26% 64% 66% 2% 2% 6% – – 24% 60% Paraná Pesquisas 1–6 May 2022 1.540 66,8% 2,7% 3% – 0,5% – 27% 63,8% 66,2% 2,5% 2,7% 2,8% – – 25,9% 63,4%...
87 KB (2,404 words) - 03:41, 14 July 2024