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Some rank six geometries for the smallest Fischer sporadic simple group | ||
| Journal of Discrete Mathematics and Its Applications | ||
| مقاله 1، دوره 10، شماره 1، خرداد 2025، صفحه 1-10 اصل مقاله (951.74 K) | ||
| نوع مقاله: Full Length Article | ||
| شناسه دیجیتال (DOI): 10.22061/jdma.2025.11584.1111 | ||
| نویسندگان | ||
| Hossein Moshtagh* 1؛ Ali Reza Rahimipour2 | ||
| 1Department of Computer Science, University of Garmsar, Address Garmsar, Semnan 3588115589, I. R. Iran | ||
| 2Faculty of Electrical & Computer Engineering, Malek Ashtar University of Technology, Tehran, I. R. Iran | ||
| تاریخ دریافت: 22 دی 1403، تاریخ بازنگری: 23 بهمن 1403، تاریخ پذیرش: 23 بهمن 1403 | ||
| چکیده | ||
| This paper introduces some new rank six geometries associated with the Fischer sporadic simple group Fi22. These geometries are both residually connected and firm, with Fi22 acts as a flag-transitive automorphism group on them. The previously known geometries for Fischer sporadic simple group Fi22 have rank at most four. Therefore, we investigate improvements to the lower bound of the maximum rank of the residually connected and firm geometries on which the group Fi22 acts as a flag-transitive automorphism group. Moreover, we demonstrate that the independent generating set of Fischer sporadic simple group Fi22 has a size of at least seven. | ||
| کلیدواژهها | ||
| sporadic simple group؛ coset geometry؛ independent generating set | ||
| مراجع | ||
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[1] R. Abbott, J. Bray, S. Linton, S. Nickerson, S.Norton, R. Parker, I. Suleiman,J. Tripp, P. Walsh, R.Wilson., ATLAS of Finite Group Representations Version 3. Available online: http://brauer.maths.qmul.ac.uk/Atlas/v3
[2] W. Bosma, J. Cannon, Handbook of Magma Functions, Department of Mathematics, University of Sydney, (1994). Available online: http://magma.maths.usyd.edu.au/magma
[3] F. Buekenhout, Handbookofincidencegeometry.Buildingsandfoundations, North-Holland, Amsterdam, (1995) 1420 pp. http://10.6.20.12:80/handle/123456789/13881
[4] F. Buekenhout, Diagrams for geometries and groups, J. Combin. Theory Ser. A 27(2) (1979) 121151. https://doi.org/10.1016/0097-3165(79)90041-4
[5] F. Buekenhout, Diagram geometries for sporadic groups, Contemp. Math. 45 (1985)1–32. https://doi.org/10.1090/conm/045/822231
[6] F. Buekenhout, D.Leemans,AranksixgeometryrelatedtotheMcLaughlinsporadicsimplegroup, Des. Codes Cryptogr, 44(1-3) (2007) 151–155. https://doi.org/10.1007/s10623-007-9082-5
[7] P. J. Cameron, P. Cara, Independent generating sets and geometries for symmetric groups, J. Algebra 258(2) (2002) 641–650. https://doi.org/10.1016/s0021-8693(02)00550-1
[8] J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, R. A. Wilson, An Atlas of Finite Groups, Oxford: Oxford University Press, (1985).https://doi.org/10.1017/S001309150002839X
[9] D. Leemans, The rank 2 geometries of the simple Suzuki groups Sz(q), Beitrage Algebra Geom. 39(1) (1998) 97–120. https://www.emis.de/journals/BAG/vol.39/no.1/10
[10] D. Leemans, On a rank four geometry for the Hall-Janko sporadic group, J. Combin. Theory Ser. 101(1) (2003) 160–167. https://doi.org/10.1016/s0097-3165(02)00022-5
[11] D. Leemans, Two rank six geometries for the Higman-Sims sporadic group, Discrete Math. 294(12) (2005) 123–132. https://doi.org/10.1016/j.disc.2004.04.041
[12] D.Leemans,AfamilyofgeometriesrelatedtotheSuzukitower, Comm.Algebra33(7)(2005)22012217. https://doi.org/10.1081/agb-200063575
[13] D. Leemans, B. G. Rodrigues, On primitive geometries of rank two, Art Discrete Appl. Math. 2(1) (2019) P1.08, 12 pp. https://doi.org/10.26493/2590-9770.1301.165
[14] A. A. Ivanov, Geometry of sporadic groups, I. Petersen and tilde geometries, Encyclopedia of Mathematics and its Applications, 76. Cambridge University Press, Cambridge, 1999. https://doi.org/10.1017/cbo9780511525933
[15] A. Pasini, Diagram geometries, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1994.https://doi.org/10.1093/oso/9780198534976.001.0001
[16] M. Ronan, G. Stroth, Minimal parabolic geometries for the sporadic groups, Europ. J. Comb. 5 (1984) 59–92. https://doi.org/10.1016/s0195-6698(84)80020-7
[17] J. Tits, Geometries polyedriques et groupes simples, Atti a Riunione Groupem. Math. Express. Lat. Firenze (1963) 66–88. https://api.semanticscholar.org/CorpusID:117201852 | ||
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