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AIMS Mathematics

2019, Volume 4, Issue 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
  • Received: 07 April 2019 Accepted: 14 August 2019 Published: 02 September 2019

  • MSC : 05B05

  • 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 $[1;31;31;31;31;31;31;31;31;, 31]$.

    Citation: Menderes Gashi. On the symmetric block design with parameters (280,63,14) admitting a Frobenius group of order 93[J]. AIMS Mathematics, 2019, 4(4): 1258-1273. doi: 10.3934/math.2019.4.1258

    Related Papers:

  • 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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    [1] M. Aschbacher, On Collineation Groups of Symmetric Block Designs, J. Comb. Theory A, 11 (1971), 272-281. doi: 10.1016/0097-3165(71)90054-9
    [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. doi: 10.1016/0012-365X(94)90103-1
    [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. doi: 10.1016/S0167-5060(08)70919-1
    [11] C. W. H. Lam, The search for a finite projective plane of order 10, Am. Math. Mon, 98 (1991), 305-318. doi: 10.1080/00029890.1991.12000759
    [12] E. Lander, Symmetric designs: An algebraic approach, Cambridge University Press, 1983.
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