The Alperin and Dade Conjectures for the O'Nan and Rudivalis Simple Groups

References

• Alperin , J. L. 1987 . Weights for Finite Groups. In The Arcata Conference on Representations of Finite Groups . Proc. of Symposia in Pure Math. , 47 : 369 – 379 .
   Google Scholar
• An , Jianbei and O'Brien , E. A. 1997 . A Local Strategy to Decide the Alperin and Dade Conjectures . J. Algebra , 189 : 34 – 57 .
   Web of Science ®Google Scholar
• An , Jianbei and O'Brien , E. A. 1999 . The Alperin and Dade Conjectures for the Fischer Simple Group Fi23 . International J. Algebra Comput. , 6 : 621 – 670 .
   Web of Science ®Google Scholar
• Bosma , Wieb and Cannon , John . 1997 . Playoust, Catherine. The MAGMA Algebra System I: The User Language . J. Symbolic Comput. , 24 : 235 – 265 .
   Web of Science ®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
• Celler , Frank , Leedham-Green , Charles R. , Murray , Scott H. , Niemeyer , Alice C. and O'Brien , E. A. 1995 . Generating random elements of a finite group . Comm. Algebra , 23 : 4931 – 4948 .
   Web of Science ®Google Scholar
• Dade , E. C. 1992 . Counting Characters in Blocks, I . Invent. Math. , 109 : 187 – 210 .
   Web of Science ®Google Scholar
• Dade , E. C. 1994 . Counting Characters in Blocks, II . J. Reine Angew. Math. , 448 : 97 – 190 .
   Web of Science ®Google Scholar
• Dade , E. C. 1996 . Counting Characters in Blocks with Cyclic Defect Groups, I . J. Algebra , 186 : 934 – 969 .
   Web of Science ®Google Scholar
• Dade , E. C. 1997 . “ Counting Characters in Blocks. II.9 ” . In Representation Theory of Finite Groups , 45 – 59 . Berlin : Walter de Gruyter . Ohio State Univ. Math. Res. Inst. Publ. 6, Columbus, OH, 1995
   Google Scholar
• The GAP Team . 2000 . GAP—Groups, Algorithms, and Programming, Version 4. Lehrstuhl D für Mathematik, RWTH Aachen, and School of Mathematical and Computational Sciences , University of St Andrews .
   Google Scholar
• Soicher , L. H. 1987 . Presentations of Some Finite Simple Groups with Applications to the O'Nan Simple Group . J. Algebra , 108 : 310 – 316 .
   Web of Science ®Google Scholar
• Ivanov , A. A. , Tsaranov , S. V. and Shpektorov , S. V. 1986 . Maximal Subgroups of the O'Nan-Sims Sporadic Simple Group and its Automorphism Group . Dokl. Akad. Nauk SSSR , 291 : 777 – 780 .
   Google Scholar
• Uno , K. 1994 . Dade's Conjecture for Tame Blocks . Osaka J. Math. , 31 : 747 – 772 .
   Web of Science ®Google Scholar
• Wilson , R. A. 1987 . The Local Subgroups of the Fischer Groups . J. London Math. Soc. , 36 : 77 – 94 .
   Web of Science ®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. 1984 . The Geometry and Maximal Subgroups of the Simple Groups of A . Rudvalis and J. Tits. Proc. London Math. Soc. , 48 : 533 – 563 .
   Web of Science ®Google Scholar
• Wilson , R. A. 1985 . The Maximal Subgroups of the O'Nan Group . J. Algebra , 97 : 467 – 473 .
   Web of Science ®Google Scholar
• Yoshiara , Satoshi . 1985 . The Maximal Subgroups of the Sporadic Simple Group of O'Nan . J. Fac. Sci. Univ. Tokyo , 32 : 105 – 141 .
   Google Scholar