Maniplexes with automorphism group PSL(2, q)

被引：0

作者：

Leemans, Dimitri ^{[1
]}

Toledo, Micael ^{[1
]}

机构：

[1] Univ Libre Bruxelles, Dept Math, CP 216 Algebre & Combinatoire,Blvd Triomphe, B-1050 Brussels, Belgium

来源：

DISCRETE MATHEMATICS | 2023年 / 346卷 / 09期

关键词：

Regular maniplex; Polytope; Projective linear group; Automorphism group; POLYTOPES; MAPS;

D O I：

10.1016/j.disc.2023.113527

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A maniplex of rank n is a combinatorial object that generalises the notion of a rank n abstract polytope. A maniplex with the highest possible degree of symmetry is called regular. In this paper we prove that there is a rank 4 regular maniplex with automorphism group PSL2(q) for infinitely many prime powers q, and that no regular maniplex of rank n > 4 exists that has PSL2(q) as its full automorphism group.& COPY; 2023 Elsevier B.V. All rights reserved.

引用

页数：8

共 50 条

[21] Hermitian codes with automorphism group isomorphic to PGL(2, q) with q odd
Korchmaros, Gabor
Speziali, Pietro
FINITE FIELDS AND THEIR APPLICATIONS, 2017, 44 : 1 - 17
[22] Halving PSL(2, q)
Bierbrauer J.
Edel Y.
Journal of Geometry, 1999, 64 (1-2) : 51 - 54
[23] Steiner systems with automorphism groups PSL(2, 71), PSL(2, 83), and P∑L(2, 35)
Betten A.
Laue R.
Molodtsov S.
Wassermann A.
Journal of Geometry, 2000, 67 (1-2) : 35 - 41
[24] Groupoids of order q(q+/-1)/2, q=2(r), with automorphism group isomorphic to SL(2,q)
Ilinykh, AP
SIBERIAN MATHEMATICAL JOURNAL, 1995, 36 (06) : 1159 - 1163
[25] Blocking semiovals in PG(2, q2), q odd, admitting PGL(2, q) as an automorphism group
Bartoli, Daniele
Pavese, Francesco
FINITE FIELDS AND THEIR APPLICATIONS, 2018, 54 : 315 - 334
[26] PSL(2,Q) AS AN IMAGE OF THE EXTENDED MODULAR GROUP WITH APPLICATIONS TO GROUP-ACTIONS ON SURFACES
SINGERMAN, D
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 1987, 30 : 143 - 151
[27] n-RECOGNITION BY PRIME GRAPH OF THE SIMPLE GROUP PSL(2,q)
Khosravi, Behrooz
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2008, 7 (06) : 735 - 748
[28] PSL(2,Q) AS A COLLINEATION GROUP OF PROJECTIVE-PLANES OF SMALL ORDER
MOORHOUSE, GE
GEOMETRIAE DEDICATA, 1989, 31 (01) : 63 - 88
[29] Finite projective planes admitting a projective linear group PSL(2, q)
Liu, WJ
Li, JL
LINEAR ALGEBRA AND ITS APPLICATIONS, 2006, 413 (01) : 121 - 130
[30] Quadruple systems of the projective special linear group PSL(2,q), q ≡ 1 (mod 4)
Keranen, MS
Kreher, DL
Shiue, PJS
JOURNAL OF COMBINATORIAL DESIGNS, 2003, 11 (05) : 339 - 351

← 1 2 3 4 5 →