Some new 3-designs invariant under the groups Sz(8) and S6(2)

被引：0

作者：

Rahimipour, Ali Reza ^{[1
]}

Adeli, Morteza ^{[2
]}

机构：

[1] Univ Qom, Fac Sci, Dept Math, POB 37161-46611, Qom, Iran

[2] Malek Ashtar Univ Technol, Fac Elect & Comp Engn, Tehran, Iran

来源：

DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS | 2024年 / 16卷 / 04期

关键词：

3-Design; permutation representation; Suzuki group; symplectic group; T-DESIGNS;

D O I：

10.1142/S1793830923500350

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we determine all simple block-transitive 3-designs on 65 points with block stabilizer of order greater than 2, admitting the 2-transitive action of the group S-z(8). As a result, we find 23 3-designs on 65 points that have Sz(8) as an automorphism group. Also we construct four 3-(36, 18, ?(1)) designs for ?(1) ? {768, 5184,6912, 9216} and two 3-(36, 17, ?(2)) designs for ?(2) ? {2880, 8640}. All of these designs have S6(2) as the full automorphism group. Some of these designs are flag and anti-flag-transitive.

引用

页数：9

共 5 条

[1] Classifying 3- and 4-designs on 28 points invariant under the group S6(2)
Rahimipour, Ali Reza
Moshtagh, Hossein
DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, 2020, 12 (03)
[2] SOME IRREDUCIBLE 2-MODULAR CODES INVARIANT UNDER THE SYMPLECTIC GROUP S6(2)
Chikamai, Lucy
Moori, Jamshid
Rodrigues, Bernardo G.
GLASNIK MATEMATICKI, 2014, 49 (02) : 235 - 262
[3] Simple 3-designs of PSL(2, 2n) with block size 8
Gong, Luozhong
Fan, Guobing
UTILITAS MATHEMATICA, 2018, 106 : 3 - 9
[4] 3-designs with block size 6 from PSL(2, q) and their large sets
Omidi, G. R.
Pournaki, M. R.
Tayfeh-Rezaie, B.
DISCRETE MATHEMATICS, 2007, 307 (13) : 1580 - 1588
[5] 3-Designs and Large Sets of PSL(2,2n) with Block Sizes 6
Omidi, G. R.
ARS COMBINATORIA, 2010, 94 : 3 - 11

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