Conjugacy of Subgroups of the General Linear Group

REFERENCES

• Aschbacher , M. 1984 . “On the Maximal Subgroups of the Finite Classical Groups.” . Invent. Math. , 76 : 469 – 514 . [Aschbacher 84]
   Web of Science ®Google Scholar
• Bosma , W. , Cannon , J. and Playoust , C. 1997 . “The Magma Algebra System I: The User Language.” . J. Symbolic. Commput. , 24 ( 3 ) : 235 – 265 . [Bosma et al. 97]
   Web of Science ®Google Scholar
• Butler , G. and Canon , J. J. 1982 . “Computing in Permutation and Matrix Groups I: Normal Closure, Commutator Subgroups, Series.” . Math. Comp. , 39 : 663 – 670 . [Butler and Canon 82]
   Web of Science ®Google Scholar
• Butler , G. 1982 . “Computing in Permutation and Matrix Groups II: Backtrack Algorithm.” . Math. Comp , 39 : 671 – 680 . [Butler 82]
   Web of Science ®Google Scholar
• Butler , G. 1983 . “Computing Normalisers in Permutation Groups.” . J. Algorithms , 4 : 163 – 175 . [Butler 83]
   Google Scholar
• Cannon , J. J. , Holt , D. F. , Slattery , M. and Steel , A. K. “Computing Subgroups of Low Index in a Finite Group.” [Cannon et al.], Submitted to J. Symbolic Comput.
   Google Scholar
• Cellar , F. and Leedham-Green , C. R. 1997 . “Calculating the Order of an Invertible Matrix.” . In Groups and Computation II (New Brunswick, NJ, 1995) Edited by: Finkelstein , L. and Kantor , W. M. 55 – 60 . Providence , RI : Amer. Math. Soc. . [Cellar and Leedham-Green 97]
   Google Scholar
• Eick , B. and Höofling , B. 2003 . “The Solvable Primitive Permutation Groups of Degree at most 6560.” . LMS J. Comput. Math. , 6 : 29 – 39 . [Eick and Höofling 03]
   Google Scholar
• The GAP Group . 2002 . GAP–Groups, Algorithms and Programming, Version 4.3. [GAP Group], Available from World Wide Web http://www.gap-system.org
   Google Scholar
• Glasby , S. P. and Howlett , R. B. 1997 . “Writing Representations over Minimal Fields.” . Comm. Algebra , 25 : 1703 – 1711 . [Glasby and Hewlett 97]
   Web of Science ®Google Scholar
• Glasby , S. P. , Leedham-Green , C. R. and O'Brien , E. A. “Writing a Representation over a Smaller Field Modulo Scalars.” [Glasby et al.], In preparation
   Google Scholar
• Holt , D. F. 1991 . “The Computation of Normalisers in Permutation Groups.” . J. Symbolic Comput. , 12 : 499 – 516 . [Holt 91]
   Web of Science ®Google Scholar
• Holt , D. F. , Leedham-Green , C. R. , O'Brien , E. A. and Rees , S. 1996 . “Testing Matrix Groups for Primitivity.” . J. Algebra , 184 : 795 – 817 . [Holt et al. 96a]
   Web of Science ®Google Scholar
• Holt , D. F. , Leedham-Green , C. R. , O'Brien , E. A. and Rees , S. 1996 . “Computing Matrix Group Decompositions with Respect to a Normal Subgroup.” . J. Algebra , 184 : 818 – 838 . [Holt et al. 96b]
   Web of Science ®Google Scholar
• Holt , D. F. and Rees , S. 1994 . “Testing Modules for Irreducibility.” . J. Austral. Math. Soc. Ser A , 57 : 1 – 16 . [Holt and Rees 94]
   Google Scholar
• Holt , D. F. and Roney-Dougal , C. M. “Constructing Maximal Subgroups of Black Box Classical Groups.” [Holt and Roney-Dougal], Submitted
   Google Scholar
• Kleidman , P. and Liebeck , M. 1990 . The Subgroup Structure of the Finite Classical Groups. Cambridge , , UK : Cambridge University Press. . [Kleidman and Liebeck 90]
   Google Scholar
• Leedham-Green , C. R. and O'Brien , E. A. 1997 . “Tensor Products Are Projective Geometries.” . J. Algebra , 189 : 514 – 528 . [Leedham-Green and O'Brien 97a]
   Web of Science ®Google Scholar
• Leedham-Green , C. R. and O'Brien , E. A. 1997 . “Recognising Tensor Products of Matrix Groups.” . Internat. J. Algebra Comput. , 7 : 541 – 559 . [Leedham-Green and O'Brien 97b]
   Web of Science ®Google Scholar
• Leedham-Green , C. R. and O'Brien , E. A. 2002 . “Recognising Tensor-Induced Matrix Groups.” . J. Algebra , 253 : 14 – 30 . [Leedham-Green and O'Brien 02]
   Web of Science ®Google Scholar
• Leon , J. S. 1997 . “Partitions, Refinements, and Permutation Group Computation.” . In Groups and Computation II (New Brunswick, NJ, 1995) Edited by: Finkelstein , L. and Kantor , W. M. 123 – 158 . Providence , RI : Amer. Math. Soc. . [Leon 97]
   Google Scholar
• Lidl , R. and Niederreiter , H. 1983 . Finite Fields Reading , MA : Addison-Wesley. . [Lidl and Niederreiter 83], Encyclopedia of Mathematics and Its Applications, 20
   Google Scholar
• Roney-Dougal , C. M. and Unger , W. R. 2003 . “The Primitive Affine Groups of Degree Less than 1000.” . J. Symbolic Comput. , 35 : 421 – 439 . [Roney-Dougal and Unger 03]
   Web of Science ®Google Scholar
• Rylands , L. J. and Taylor , D. E. 1998 . “Matrix Generators for the Orthogonal Groups.” . J. Symbolic Comput. , 25 : 351 – 360 . [Rylands and Taylor 98]
   Web of Science ®Google Scholar
• Taylor , D. E. 1987 . “Pairs of Generators for Matrix Groups, I.” . The Cayley Bulletin , 3 : 76 – 85 . [Taylor 87]
   Google Scholar