Flag-transitive block designs and unitary groups

被引：10

作者：

Alavi, Seyed Hassan ^{[1
]}

Bayat, Mohsen ^{[1
]}

Daneshkhah, Ashraf ^{[1
]}

机构：

[1] Bu Ali Sina Univ, Fac Sci, Dept Math, Hamadan, Hamadan, Iran

来源：

MONATSHEFTE FUR MATHEMATIK | 2020年 / 193卷 / 03期

关键词：

2-Design; Flag-transitive; Automorphism group; Almost simple group; Unitary group; Large subgroup; LAMBDA) SYMMETRIC DESIGNS; FINITE LINEAR-SPACES; AUTOMORPHISM-GROUPS; NONSYMMETRIC; 2-DESIGNS; MAXIMAL-SUBGROUPS; REPRESENTATIONS; 2-(V;

D O I：

10.1007/s00605-020-01421-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we determine all pairs (D, G), where D is a 2-design with gcd(r,.) = 1 and G is a flag-transitive almost simple automorphism group of D whose socle is PSU(n, q) with (n, q) = (3, 2). We prove that such a design belongs to one of the two infinite families of Hermitian unitals and Witt-Bose-Shrikhande spaces, or it is isomorphic to a design with parameters (6, 3, 2), (7, 3, 1), (8, 4, 3), (10, 6, 5), (11, 5, 2) or (28, 7, 2). In particular, if D is symmetric, then it is either the Fano plane with parameters (7, 3, 1), or the unique Hadamard design with parameters (11, 5, 2).

引用

页码：535 / 553

页数：19

共 33 条

[1]

Alavi SH, 2016, B IRAN MATH SOC, V42, P201

[2]

Alavi S.H., ARXIV170201257

[3]

Alavi S.H., 2019, ARXIV191106175

[4] Flag-Transitive Block Designs and Finite Simple Exceptional Groups of Lie Type [J].