AIMS Mathematics, 2019, 4(4): 1258-1273. doi: 10.3934/math.2019.4.1258

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On the symmetric block design with parameters (280,63,14) admitting a Frobenius group of order 93

Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Prishtina, Avenue “Mother Teresa” 5, 10000 Prishtina, Kosovo

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In this paper we have proved that for a putative symmetric block design ${\mathcal D}$ with parameters (280,63,14), admitting a Frobenius group $G=\langle\rho,\mu\vert \rho^{31}=\mu^{3}=1,\rho^\mu=\rho^5\rangle$ of order 93, there are exactly thirteen possible orbit structure up to isomorphism; two with the orbit distribution $[1;31;31;31;93;93]$, eight with the orbit distribution $[1;31;31;31;31;31;31;93]$ and three with the orbit distribution $[1;31;31;31;31;31;31;31;31;,31]$.
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# References

1. M. Aschbacher, On Collineation Groups of Symmetric Block Designs, J. Comb. Theory A, 11 (1971), 272-281.

2.T. Beth, D. Jungnickel and H. Lenz, Design Theory, Cambridge University Press, 1999.

3. A. Beutelspacher, Einführung in die endliche Geometrie I, Bibliographisches Institut, Mannheim-Wien-Zürich, 1985.

4. V. Cepulić, On symmetric block designs (40,13,4) with automorphisms of order 5, Discrete Math., 128 (1994), 45-60.

5.D. Crnković, Some new Menon designs with parameters (196,91,42), Math. Commun., 10 (2005), 169-175.

6.R. Gjergji, On the symmetric block design with parameters (153, 57, 21), Le Matematiche, 64 (2009), 147-159.

7.B. Huppert, Character Theory of Finite Groups, Walter de Gruyter - Berlin - New York, 1998.

8.M. Gashi, A Construction of a Symmetric Design with Parameters (195,97,48) with Help of Frobenius Group of Order 4656, International Mathematical Forum, 5 (2010), 383-388.

9.Z. Janko and T. van Trung, Construction of a New Symmetric Block Design for (78,22,6) with Help of Tactical Decompositions, J. Comb. Theory A, 40 (1995), 451-455.

10.Z. Janko, Coset Enumeration in Groups and Constructions of Symmetric Designs, Annals of Discrete Mathematics, 52 (1992), 275-277.

11. C. W. H. Lam, The search for a finite projective plane of order 10, Am. Math. Mon, 98 (1991), 305-318.

12.E. Lander, Symmetric designs: An algebraic approach, Cambridge University Press, 1983.