A NEW COMPUTER CONSTRUCTION OF THE IRREDUCIBLE 112-DIMENSIONAL 2-MODULAR REPRESENTATION OF JANKO'S GROUP J₄

REFERENCES

• Bannai , E. and Ito , T. 1984 . “ Algebraic Combinatorics I ” . In Association Schemes Menlo Park, California : Benjamin and Cummings Publishing Company .
   Google Scholar
• Benson , D. J. 1980 . The Simple Group J ₄ , PhD. Thesis Cambridge : Trinity College .
   Google Scholar
• Bosma , W. and Cannon , J. 1993 . MAGMA Handbook Sydney
   Google Scholar
• Butler , G. 1991 . “ Fundamental algorithms for permutation groups ” . In Lect. Notes in Computer Science Heidelberg : Springer Verlag .
   Google Scholar
• Cooperman , G. , Finkelstein , L. , Tselman , M. and York , B. 1997 . Constructing permutation representations for large matrix groups . J. Symbolic Computation , 24 : 471 – 488 .
   Google Scholar
• Cooperman , G. , Lempken , W. , Michler , G. O. and Weller , M. A new existence proof of Janko's sporadic simple group J 4 . Proceedings of Euro-Conference “omputational methods for representations of groups and algebras” . Edited by: Dräcler , P. , Michler , G. and Ringel , C. M. Basel : Progress in Math., Birkhäuser Verlag .
   Google Scholar
• Conway , J. H. , Curtis , R. T. , Norton , S. P. , Parker , R. A. and Wilson , R. A. 1985 . Atlas of finite groups Oxford : Clarendon Press .
   Google Scholar
• Fleischmann , P. , Michler , G. O. , Roelse , P. , Rosenboom , J. , Staszewski , R. , Wagner , C. and Weller , M. 1995 . Linear algebra over small finite fields on parallel machines 23 Heft : Vorlesungen Fachbereich Math. Univ. Essen .
   Google Scholar
• Gollan , H. W. 1995 . A new existence proof for Ly, the sporadic group of R. Lyons Preprint IEM Essen .
   Google Scholar
• Gorenstein , D. 1982 . Finite simple groups New York : Plenum Press .
   Google Scholar
• Gorenstein , D. , Lyons , R. and Solomon , R. 1996 . The classification of the finite simple groups , Mathematical Surveys and Monographs 40, No. 2 Providence, Rhode Island : American Mathematical Society .
   Google Scholar
• Ivanov , A. A. , Linton , S. A. , Lux , K. , Saxl , J. and Soicher , L. H. 1995 . Distance-transitive representations of the sporadic groups . Communications in Algebra , 23 : 3379 – 3427 .
   Web of Science ®Google Scholar
• Janko , Z. 1976 . A new finite simple group of order 86 · 775 · 571 · 046 · 077 · 562 · 880 which possesses M 24 and the full covering group of M 22 as subgroups . J. Algebra , 42 : 564 – 596 .
   Google Scholar
• Landrock , P. 1983 . Finite group algebras and their modules Cambridge : Cambridge University Press .
   Google Scholar
• Lempken , W. 1993 . Constructing J 4 in GL(1333, 11) . Communications in Algebra , 21 : 4311 – 4351 .
   Google Scholar
• Michler , G. O. 1999 . High performance computations in group representation theory , Algorithmic algebra and number theory Edited by: Matzat , B. H. , Greuel , G. M. and Hiss , G. 399 – 415 . Heidelberg : Springer-Verlag .
   Google Scholar
• Norton , S. 1980 . The construction of J 4 . Proceedings of Symposia in Mathematics AMS , 37 : 271 – 277 .
   Google Scholar
• Weller , M. 1999 . “ Construction of large permutation representations for matrix groups ” . In Transactions of the High Performance Computing Center Stuttgart (HLRS) “High Performance Computing in Science and Engineering '98” Edited by: Krause , E. and Jäger , W. 430 – 452 . Heidelberg : Springer Verlag .
   Google Scholar
• Wilson , R. A. 1996 . Standard generators for sporadic simple groups . J. Algebra , 184 : 505 – 515 .
   Web of Science ®Google Scholar
• Wilson , R. A. Atlas of finite group representations http://www.mat.bham. ac.uk.atlas
   Google Scholar