On Generators and Representations of the Sporadic Simple Groups

REFERENCES

• Conway , J. , Curtis , R. , Norton , S. , Parker , R. , Wilson , R. ( 1985 ). Atlas of Finite Groups . Oxford : Clarendon Press .
   Google Scholar
• ATLAS of Finite Group Representations – Version 3. http://brauer.maths. qmul.ac.uk/Atlas/v3/. Accessed September 8, 2012 .
   Google Scholar
• Bosma , W. , Cannon , J. ( 1996 ). The MAGMA Handbook . Sydney : University of Sydney Press .
   Google Scholar
• Conder , M. D. E. , Wilson , R. A. , Woldar , A. J. (1992). The symmetric genus of sporadic groups. Proc. Amer. Math. Soc. 116(3):653–663.
   Google Scholar
• Dempwolff , U. ( 1987 ). Linear groups with large cyclic subgroups and translation planes . Rend. Sem. Mat. Univ. Padova 77 : 69 – 113 .
   Google Scholar
• Di Martino , L. , Zalesski , A. E. ( 2012 ). Unipotent elements in representations of finite groups of Lie type . Journal of Algebra and Its Applications 11 ( 2 ): 1250038 .
   Web of Science ®Google Scholar
• Di Martino , L. , Zalesski , A. E. Almost cyclic elements in Weil representations of finite classical groups (in preparation) .
   Google Scholar
• Ganief , S. , Moori , J. ( 1997 ). (p, q, r)-generations of the smallest Conway group Co 3 . J. Algebra 188 ( 2 ): 516 – 530 .
   Web of Science ®Google Scholar
• The GAP Group . ( 2012 ). GAP – Groups, Algorithms, and Programming, Version 4.5.4. Available at http://www.gap-system.org. Accessed July 16, 2012 .
   Google Scholar
• Guralnick , R. , Penttila , T. , Praeger , C. , Saxl , J. ( 1999 ). Linear groups having certain large prime divisors . Proc. London Math. Soc. (3) 78 : 167 – 214 .
   Web of Science ®Google Scholar
• Guralnick , R. , Saxl , J. ( 2001 ). Generation of finite almost simple groups by conjugates . J. Algebra 268 : 519 – 571 .
   Web of Science ®Google Scholar
• Hiss , G. , Malle , G. ( 2002/2003 ). Low-dimensional representations of quasi-simple groups. LMS J. Comput. Math 4:22–63. (Corrigenda: LMS J. Comput. Math. 5:95–126.)
   Google Scholar
• Jansen , C. ( 2005 ). The minimal degrees of faithful representations of the sporadic simple groups and their covering groups . LMS J. Comput. Math. 8 : 122 – 144 .
   Google Scholar
• Noeske , F. ( 2007 ). The 2- and 3-modular characters of the sporadic simple Fischer group Fi 22 and its cover . J. Algebra 309 : 723 – 743 .
   Web of Science ®Google Scholar
• Tiep , P. H. , Zalesskiĭ , A. E. ( 2000 ). Some aspects of finite linear groups: A survey. J. Math. Sciences. Vol. 100. pp. 1893–1914. (Russian edition: Contemporary Mathematics and its Applications. Thematic Surveys. Vol. 58, Algebra - 12.)
   Google Scholar
• Wagner , A. ( 1978 ). Collineation groups generated by homologies of order greater than 2 . Geom. Dedicata 7 : 387 – 398 .
   Google Scholar
• Wagner , A. ( 1980/1981 ). Determination of the finite primitive reflection groups over an arbitrary field of characteristic not two . Parts I, II, III, Geom. Dedic. 9 : 239 – 253 , 10:191–203, 475–523 .
   Google Scholar
• Ward , J. M. ( 2009 ). Generation Of Simple Groups by Conjugate Involutions. PhD Thesis (QMC, University of London) .
   Google Scholar
• Wilson , R. A. ( 2009 ). The Finite Simple Groups . Graduate Texts in Mathematics . Vol. 251 . London : Springer-Verlag London, Ltd .
   Google Scholar
• Zalesskiĭ , A. E. ( 1999 ). Minimal polynomials and eigenvalues of p-elements in representations of quasi-simple groups with a cyclic Sylow p-subgroup . J. London Math. Soc. (2) 59 ( 3 ): 845 – 866 .
   Web of Science ®Google Scholar
• Zalesski , A. E. ( 2009 ). On eigenvalues of group elements in representations of simple algebraic groups and finite Chevalley groups . Acta Applicanda Mathematicae 108 : 175 – 195 .
   Web of Science ®Google Scholar
• Zalesskiĭ , A. E. , Serezhkin , V. N. ( 1976 ). Linear groups generated by transvections . Math. USSR, Izvestija 10 : 25 – 46 .
   Web of Science ®Google Scholar
• Zisser , I. ( 1989 ). The covering numbers of the sporadic simple groups . Israel J. Math. 67 ( 2 ): 217 – 224 .
   Web of Science ®Google Scholar
• Communicated by S. Sehgal.
   Google Scholar