The Higman-Sims sporadic simple group as the automorphism group of resolvable $3$-designs

Rahimipour, Ali Reza

doi:10.22108/toc.2023.132404.1956

تعداد نشریات	43
تعداد شماره‌ها	1,705
تعداد مقالات	13,959
تعداد مشاهده مقاله	33,467,941
تعداد دریافت فایل اصل مقاله	13,270,224

	The Higman-Sims sporadic simple group as the automorphism group of resolvable $3$-designs
Transactions on Combinatorics
مقاله 5، دوره 13، شماره 2، شهریور 2024، صفحه 153-164 اصل مقاله (462.98 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2023.132404.1956
نویسنده
Ali Reza Rahimipour^*
Department of Mathematics, Faculty of Science, University of Qom, P.O. Box 37161−46611, Qom, I. R. Iran
چکیده
Presenting sporadic simple groups as an automorphism groups of designs and graphs is an exciting field in finite group theory.In this paper, with two different methods, we present some new resolvable simple $3$-designs with Higman-Sims sporadic simple group $\rm HS$ as the full automorphism group.Also, we classify all block-transitive self-orthogonal designs on 176 points with even block size that admit sporadic simple group $\rm HS$ as an automorphism group. Furthermore, with these methods we construct some new resolvable $3$-designs on 36, 40, 120 and 176 points.
کلیدواژه‌ها
$t$-design؛ resolvable design؛ sporadic simple group

مراجع
[1] R. Abbott, J. Bray, S. Linton, S. Nickerson, S.Norton, R. Parker, I. Suleiman, J. Tripp, P. Walsh and R.Wilson, Atlas of Finite Group Representations Version 3, Available online http://brauer.maths.qmul.ac.uk/Atlas/v3/. [2] W. O. Alltop, Extending t-designs, J. Combinatorial Theory Ser. A, 18 (1975) 177–186. [3] M. Araya, M. Harada, V. D. Tonchev and A. Wassermann, Mutually disjoint designs and new 5-designs derived from groups and codes, J. Combin. Des., 18 (2010) 305–317. [4] A. Betten, R. Laue and A. Wassermann, Simple 7-designs with small parameters, J. Combin. Des., 7 (1999) 79–94. [5] W. Bosma and J. J. Cannon, Handbook of Magma functions, School of Mathematics and Statistics, University of Sydney, Sydney, 1995. [6] P. J. Cameron and J. H. van Lint, Designs, Graphs, Codes and their Links, London Mathematical Society Student Texts, 22, Cambridge University Press, Cambridge, 1991. [7] N. Chigira, M. Harada and M. Kitazume, Permutation groups and binary self-orthogonal codes, J. Algebra, 309 (2007) 610–621. [8] C. J. Colbourn and J. H. Dinitz (eds.), Handbook of combinatorial designs, 2nd ed., Chapman & Hall/CRC, Boca Raton, FL, (2007). [9] J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, An Atlas of Finite Groups, Oxford: Oxford University Press, (1985). [10] E. S. Kramer and D. M. Mesner, t-designs on hypergraphs, Discrete Math., 15 (1976) 263–296. [11] V. Krčadinac and R. Vlahović, New quasi-symmetric designs by the Kramer-Mesner method, Discrete Math., 339 (2016) 2884–2890. [12] D. L. Kreher and S. P. Radziszowski, Constructing 6-(14, 7, 4) designs, Finite geometries and combinatorial designs (Lincoln, NE, 1987), 137-151, Contemp. Math., 111, Amer. Math. Soc., Providence, RI, (1990). [13] A. R. Rahimipour and H. Moshtagh, Classifying 3- and 4-designs on 28 points invariant under the group S6 (2), Discrete Math. Algorithm. Appl., 12 (2020) 6 pp. [14] V. D. Tonchev, A characterization of designs related to the Witt system S(5, 8, 24), Math. Z., 191 (1986) 225–230. [15] TheGAPTeam,GAP–Groups,Algorithms,andProgramming,Version4.10.1, (http://www.gap-system.org).
آمار تعداد مشاهده مقاله: 142 تعداد دریافت فایل اصل مقاله: 206

سامانه مدیریت نشریات علمی. طراحی و پیاده سازی از سیناوب

پیوندهای مفید

اخبار و اعلانات

آمار

The Higman-Sims sporadic simple group as the automorphism group of resolvable $3$-designs