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

Research article

Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

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

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 $[1;31;31;31;31;31;31;31;31;,31]$.
  Article Metrics


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.

© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (

Download full text in PDF

Export Citation

Article outline

Show full outline
Copyright © AIMS Press All Rights Reserved