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Designs, Codes and Cryptography

Erschienen in:

01.12.2016

Flag-transitive non-symmetric 2-designs with \((r,\lambda )=1\) and sporadic socle

verfasst von: Xiaoqin Zhan, Shenglin Zhou

Erschienen in: Designs, Codes and Cryptography | Ausgabe 3/2016

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This paper is a contribution to the investigation of flag-transitive non-symmetric 2-designs. We prove that if \({\mathcal {D}}\) is a non-trivial non-symmetric 2-\((v,k,\lambda )\) design with \((r,\lambda )=1\) and \(G\le Aut({\mathcal {D}})\) is flag-transitive with sporadic socle, then \({\mathcal {D}}\) must be one of following: a 2-(12, 6, 5) design with \(G=M_{11}\), or a 2-(22, 6, 5) design with \(G=M_{22}\) or \(M_{22}:2\).

Vorheriger Artikel On the geometric constructions of optimal linear codes

Nächster Artikel Total perfect codes in Cayley graphs

Bosma W., Cannon J., Playoust C.: The MAGMA algebra system I: the user language. J. Symb. Comput. 24, 235–265 (1997).

Bray J.N., Wilson R.A.: Explicit representations of the maximal subgroups of the Monster. J. Algebra 300(2), 834–857 (2006).

Buekenhout F., Delandtsheer A., Doyen J., Kleidman P.B., Liebeck M., Saxl J.: Linear spaces with flag-transitive automorphism groups. Geom. Dedicata 36, 89–94 (1990).

Camina A.R., Spiezia F.: Sporadic groups and automorphisms of linear spaces. J. Comb. Des. 8(5), 353–362 (2000).

Colbourn C.J., Dinitz J.H.: The CRC Handbook of Combinatorial Designs. CRC Press, Boca Raton (1996).

Conway J.H., Curtis R.T., Norton S.P., Parker R.A., Wilson R.A.: Atlas of Finite Groups. Oxford University Press, London (1985).

Davies H.: Flag-transitivity and primitivity. Discret. Math. 63, 91–93 (1987).

Davies H.: Automorphisms of Designs. Ph.D. Thesis, University of East Anglia (1987).

Dembowski P.: Finite Geometries. Springer, New York (1968).

10.

The GAP Group, GAP-Groups, Algorithms, and Programming, Version 4.4, 2005. http://www.gap-system.org

11.

Tian D., Zhou S.: Flag-transitive 2-\((v, k,\lambda )\) symmetric designs with sporadic socle. J. Comb. Des. 23(4), 140–150 (2015).

12.

Wielandt H.: Finite Permutation Groups. Academic Press, New York (1964).

13.

Zhou S., Wang Y.: Flag-transitive non-symmetric 2-designs with \((r,\lambda )=1\) and alternating socle. Electron. J. Comb. 22, #P2.6 (2015).

14.

Zhu Y., Guan H., Zhou S.: Flag-transitive 2-\((v, k,\lambda )\) symmetric designs with \((r,\lambda )=1\) and alternating socle. Front. Math. China 10(6), 1483–1496 (2015).

15.

Zieschang P.H.: Flag transitive automorphism groups of 2-designs with \((r,\lambda )=1\). J. Algebra 118, 265–275 (1988).

Titel: Flag-transitive non-symmetric 2-designs with and sporadic socle
verfasst von: Xiaoqin Zhan
Shenglin Zhou
Publikationsdatum: 01.12.2016
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 3/2016
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-015-0171-6

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Flag-transitive non-symmetric 2-designs with \((r,\lambda )=1\) and sporadic socle

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