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Designs from maximal subgroups and conjugacy classes of $\mathrm{PSL}(2,q)$, $q$ odd | ||
| AUT Journal of Mathematics and Computing | ||
| مقاله 5، دوره 4، شماره 1، 2023، صفحه 47-55 اصل مقاله (390.12 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2022.21877.1117 | ||
| نویسندگان | ||
| Xavier Mbaale1؛ Bernardo G. Rodrigues2؛ Seiran Zandi* 3 | ||
| 1Department of Mathematics and Statistics, University of Zambia, Lusaka, Zambia | ||
| 2Department of Mathematics and Applied Mathematics, University of Pretoria, Hatfield 0028, South Africa | ||
| 3Farzanegan1 High School, Sanandaj, Kurdistan, Iran | ||
| چکیده | ||
| In this paper, using a method of construction of $1$-designs which are not necessarily symmetric, introduced by Key and Moori, we determine a number of $1$-designs with interesting parameters from the maximal subgroups and the conjugacy classes of elements of the group $PSL(2,q)$ for $q$ a power of an odd prime. | ||
| کلیدواژهها | ||
| Linear group؛ design؛ conjugacy class؛ maximal subgroup؛ primitive permutation representation | ||
| مراجع | ||
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[1] E. F. Assmus, Jr. and J. D. Key, Designs and their codes, vol. 103 of Cambridge Tracts in Mathematics, Cambridge University Press, Cambridge, 1992.
[2] J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, and R. A. Wilson, ATLAS of finite groups, Oxford University Press, Eynsham, 1985. Maximal subgroups and ordinary characters for simple groups, With computational assistance from J. G. Thackray.
[3] M. R. Darafsheh, Designs from the group PSL2(q), q even, Des. Codes Cryptogr., 39 (2006), pp. 311–316.
[4] L. E. Dickson, Linear groups: With an exposition of the Galois field theory, Dover Publications, Inc., New York, 1958. With an introduction by W. Magnus.
[5] T. Fritzsche, The depth of subgroups of PSL(2, q), J. Algebra, 349 (2012), pp. 217–233.
[6] B. Huppert, Endliche Gruppen. I, Die Grundlehren der mathematischen Wissenschaften, Band 134, Springer[1]Verlag, Berlin-New York, 1967.
[7] I. M. Isaacs, Character theory of finite groups, Dover Publications, Inc., New York, 1994. Corrected reprint of the 1976 original [Academic Press, New York; MR0460423 (57 #417)].
[8] J. D. Key and J. Moori, Codes, designs and graphs from the Janko groups J1 and J2, J. Combin. Math. Combin. Comput., 40 (2002), pp. 143–159.
[9] , Designs from maximal subgroups and conjugacy classes of finite simple groups, J. Combin. Math. Combin. Comput., 99 (2016), pp. 41–60.
[10] J. D. Key, J. Moori, and B. G. Rodrigues, On some designs and codes from primitive representations of some finite simple groups, J. Combin. Math. Combin. Comput., 45 (2003), pp. 3–19. [
11] O. H. King, The subgroup structure of finite classical groups in terms of geometric configurations, in Surveys in combinatorics 2005, vol. 327 of London Math. Soc. Lecture Note Ser., Cambridge Univ. Press, Cambridge, 2005, pp. 29–56.
[12] X. Mbaale and B. G. Rodrigues, Symmetric 1-designs from PSL2(q), for q a power of an odd prime, Trans. Comb., 10 (2021), pp. 43–61.
[13] J. Moori, Finite groups, designs and codes, in Information security, coding theory and related combinatorics, vol. 29 of NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur., IOS, Amsterdam, 2011, pp. 202–230.
[14] , Designs and codes from P SL2(q), in Group theory, combinatorics, and computing, vol. 611 of Contemp. Math., Amer. Math. Soc., Providence, RI, 2014, pp. 137–149.
[15] J. Moori and B. G. Rodrigues, A self-orthogonal doubly even code invariant under McL : 2, J. Combin. Theory Ser. A, 110 (2005), pp. 53–69.
[16] , Some designs and codes invariant under the simple group Co2, J. Algebra, 316 (2007), pp. 649–661. [
17] , A self-orthogonal doubly-even code invariant under McL, Ars Combin., 91 (2009), pp. 321–332.
[18] , On some designs and codes invariant under the Higman-Sims group, Util. Math., 86 (2011), pp. 225–239.
[19] J. Moori, B. G. Rodrigues, A. Saeidi, and S. Zandi, Some symmetric designs invariant under the small Ree groups, Comm. Algebra, 47 (2019), pp. 2131–2148.
[20] , Designs from maximal subgroups and conjugacy classes of Ree groups, Adv. Math. Commun., 14 (2020), pp. 603–611.
[21] J. Moori and A. Saeidi, Constructing some designs invariant under P SL(2, q), q even, Commun. Algebra, 46 (2018), pp. 160–166.
[22] , Some designs invariant under the Suzuki groups, Util. Math., 109 (2018), pp. 105–114.
[23] R. A. Wilson, The finite simple groups, vol. 251 of Graduate Texts in Mathematics, Springer-Verlag London, Ltd., London, 2009. | ||
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