3-Designs from PSL (2, q)

P. J. Cameron; H. R. Maimani; G. R. Omidi; B. Tayfeh-Rezaie

doi:10.1016/j.disc.2005.06.041

3-Designs from PSL (2, q)

P. J. Cameron^*, H. R. Maimani, G. R. Omidi, B. Tayfeh-Rezaie

^*Corresponding author for this work

Centre for Interdisciplinary Research in Computational Algebra

Research output: Contribution to journal › Article › peer-review

39 Citations (Scopus)

Abstract

The group PSL (2, q) is 3-homogeneous on the projective line when q is a prime power congruent to 3 modulo 4 and therefore it can be used to construct 3-designs. In this paper, we determine all 3-designs admitting PSL (2, q) with block size not congruent to 0 and 1 modulo p where q = pⁿ.

Original language	English
Pages (from-to)	3063-3073
Number of pages	11
Journal	Discrete Mathematics
Volume	306
Issue number	23 SPEC. ISS.
DOIs	https://doi.org/10.1016/j.disc.2005.06.041
Publication status	Published - 6 Dec 2006

Keywords

Automorphism groups
Möbius function
Projective special linear groups
Subgroup lattices
t-Designs

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10.1016/j.disc.2005.06.041

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abstract = "The group PSL (2, q) is 3-homogeneous on the projective line when q is a prime power congruent to 3 modulo 4 and therefore it can be used to construct 3-designs. In this paper, we determine all 3-designs admitting PSL (2, q) with block size not congruent to 0 and 1 modulo p where q = pn.",

keywords = "Automorphism groups, M{\"o}bius function, Projective special linear groups, Subgroup lattices, t-Designs",

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AU - Cameron, P. J.

AU - Maimani, H. R.

AU - Omidi, G. R.

AU - Tayfeh-Rezaie, B.

PY - 2006/12/6

Y1 - 2006/12/6

N2 - The group PSL (2, q) is 3-homogeneous on the projective line when q is a prime power congruent to 3 modulo 4 and therefore it can be used to construct 3-designs. In this paper, we determine all 3-designs admitting PSL (2, q) with block size not congruent to 0 and 1 modulo p where q = pn.

AB - The group PSL (2, q) is 3-homogeneous on the projective line when q is a prime power congruent to 3 modulo 4 and therefore it can be used to construct 3-designs. In this paper, we determine all 3-designs admitting PSL (2, q) with block size not congruent to 0 and 1 modulo p where q = pn.

KW - Automorphism groups

KW - Möbius function

KW - Projective special linear groups

KW - Subgroup lattices

KW - t-Designs

U2 - 10.1016/j.disc.2005.06.041

DO - 10.1016/j.disc.2005.06.041

M3 - Article

AN - SCOPUS:33750284685

SN - 0012-365X

VL - 306

SP - 3063

EP - 3073

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 23 SPEC. ISS.

ER -

3-Designs from PSL (2, q)

Abstract

Keywords

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